1. GR Group Theory group theory section of the mathematics eprint arXiv. http://front.math.ucdavis.edu/math.GR

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ GR Group Theory Calendar Search Authors: All AB CDE FGH ... U-Z New articles (last 12) 3 Jun math.GR/0406046 Higher Dimensional Thompson Groups. Matthew G. Brin . 27 pages. GR 3 Jun math.GR/0406044 On the Zappa-Szep Product. Matthew G. Brin . 29 pages. GR CT 3 Jun math.GR/0406043 The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand. Matthew G. Brin . 15 pages. GR 3 Jun math.GR/0406042 The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V. Matthew G. Brin . 27 pages. GR 2 Jun math.GR/0406014 Special involutions and bulky parabolic subgroups in finite Coxeter groups. Goetz Pfeiffer , Gerhard Roehrle . 6 pages. 2004/13. GR 2 Jun math.GR/0406013 Growth rates of amenable groups. Goulnara Arzhantseva , Victor Guba , Luc Guyot . 6 pages. GR 1 Jun math.GR/0405590 Twisted conjugacy classes of automorphisms of Baumslag-Solitar groups. Alexander Fel'shtyn , Daciberg L. Goncalves . 13 pages. MPi-2004-32. GR GT Cross-listings 3 Jun math.NT/0406048 Zeros of polynomials over Cayley-Dickson algebras. S. V.

2. The Dog School Of Mathematics Presents Introduction to group theory. This is intended to be an introduction togroup theory. The chapters so far are Introduction to group theory. http://members.tripod.com/~dogschool/

The Dog School of Mathematics presents Introduction to Group Theory This is intended to be an introduction to Group Theory. My hope is to provide a clear passage to understanding introductory group theory. The project will expand as time goes by. The chapters so far are: Introduction to Group Theory 1. What is Group Theory 2. Examples of Groups 3. Housekeeping Theorems 4. Cayley Tables ... 14. Solve the Cube 1 Send comments, corrections and criticisms to: dogschool@dog.com This page has been visited times. var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded"

3. The Geometry Junkyard: Symmetry And Group Theory Symmetry and group theory. The Aesthetics of Symmetry, essay and design tips by Jeff Chapman labeling edges of platonic solids with numbers, and their connections with group theory http://www.ics.uci.edu/~eppstein/junkyard/sym.html

Symmetry and Group Theory The Aesthetics of Symmetry , essay and design tips by Jeff Chapman. Antipodes . Jim Propp asks whether the two farthest apart points, as measured by surface distance, on a symmetric convex body must be opposite each other on the body. Apparently this is open even for rectangular boxes. Associating the symmetry of the Platonic solids with polymorf manipulatives. Border pattern gallery . Oklahoma State U. class project displaying examples of the seven types of symmetry (frieze groups) possible for linear patterns in the plane. Box of Mirrors . Renderings of 3d reflection groups. The California Math Show goes to Spain . Photo exhibit of various symmetric patterns found in the architecture of Granada. Cognitive Engineering Lab , Java applets for exploring tilings, symmetry, polyhedra, and four-dimensional polytopes. Conceptual proof that inversion sends circles to circles , G. Kuperberg. Convex Archimedean polychoremata , 4-dimensional analogues of the semiregular solids, described by Coxeter-Dynkin diagrams representing their symmetry groups. Crystallographic topology . C. Johnson and M. Burnett of Oak Ridge National Lab use topological methods to understand and classify the symmetries of the lattice structures formed by crystals. (Somewhat technical.) Crystallography now , tutorial on the seventeen plane symmetry groups by George Baloglou.

4. 20: Group Theory And Generalizations Selected topics here 20 group theory and Generalizations. Introduction group theory can be considered the study of symmetry the collection of symmetries of some polyhedra). Interestingly http://www.math.niu.edu/~rusin/known-math/index/20-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 20: Group Theory and Generalizations Introduction Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way. Formally, a group is a set G on which there is a multiplication '*' defined, satisfying the associative law. In addition, there is to be an element '1' in G with 1*g=g*1=g for every g in G; and every element g in G must have an inverse h satisfying g*h=h*g=1. A particularly important class of groups is the set of permutation groups, those in which the elements are permutations of some set, and the group operation is simply composition. For example, the symmetric group on N objects is the set of all N! rearrangements of the N elements. Other important examples include the alternating groups and the Mathieu groups. In some sense, every group is a permutation group, but interesting questions arise in relation to the action on the set. For example, one considers groups which are highly transitive (they include enough symmetries to permute many large subsets), or groups which preserve additional structure of the set being permuted (angles in space, for example). Many combinatorial questions can be reduced to questions about the symmetric group; even the Rubik's cube can be viewed as a puzzle concerning a particular permutation group.

5. Group Theory Symmetry in Chemistry group theory. group theory is one of the most powerful mathematical tools used in Quantum The key to applying group theory is to be able to identify http://www.science.siu.edu/chemistry/tyrrell/group_theory/sym1.html

Go to.... Home Free JavaScripts provided by The JavaScript Source Symmetry in Chemistry - Group Theory Group Theory is one of the most powerful mathematical tools used in Quantum Chemistry and Spectroscopy. It allows the user to predict, interpret, rationalize, and often simplify complex theory and data. At its heart is the fact that the Set of Operations associated with the Symmetry Elements of a molecule constitute a mathematical set called a Group . This allows the application of the mathematical theorems associated with such groups to the Symmetry Operations All Symmetry Operations associated with isolated molecules can be characterized as Rotations: (a) Proper Rotations : C n k ; k = 1,......, n When k = n, C n k = E, the Identity Operation n indicates a rotation of 360/n where n = 1,.... (b) Improper Rotations : S n k , k = 1,....., n When k = 1, n = 1 S n k = s , Reflection Operation When k = 1, n = 2 S n k = i , Inversion Operation In general practice we distinguish Five types of operation: (i) E , Identity Operation (ii) C n k , Proper Rotation about an axis

6. Group Pub Forum Home Page These are the community pages for group theory, the mathematics of symmetry. group theory is a branch of algebra, but has strong connections with almost all parts of mathematics. .uk is for the http://www.bath.ac.uk/~masgcs/gpf.html

Group Pub Forum Home Page The mailing list group-pub-forum@maths.bath.ac.uk is for the discussion of any aspect of Group Theory. The reason for the name is that the spirit is supposed to be that of a conversation in a pub at a Group Theory conference. The forum has over 400 members world-wide. If installing a link to Group Pub Forum, please link to this page; the directory structure of other pages is not guaranteed to be stable. Archive of GPF email (currently not working) Mathematical Resources Books and Journals Problem Book ... The Landlord Anti-pollution measures: In order to eliminate spam (electronic junk mail), the mailing list has now become closed. This means that if you send mail from address which a subscriber has registered, everything will be as before. If you use an unregistered account address, the mail will first go to the landlord for approval. Anything related to group theory will then be forwarded to the list. Simultaneously, any address casually used by a subscriber will be added to the list of approved addresses, so that in future email from that source will be allowed straight into the mailing list. Additionally, if you wish to register alternate sender addresses now, please send them to group-landlord@maths.bath.ac.uk with `extra addresses' in the subject line. If you have any suggestions for improvements in this web site, or wish to report a known or suspected bug, please send

7. Geometric Group Theory Geometric group theory. The Geometric group theory Page provides informationand resources about geometric group theory and lowdimensional http://www.math.ucsb.edu/~jon.mccammond/geogrouptheory/

Home People Organizations Conferences ... Resources Geometric Group Theory The Geometric Group Theory Page provides information and resources about geometric group theory and low-dimensional topology, although the links sometimes stray into neighboring fields. This page is meant to help students, scholars, and interested laypersons orient themselves to this large and ever-expanding body of work. Click below for information about the following areas: People : Names and web pages of geometric group theorists around the world Organizations : Institutions where geometric group theory is studied, as well as general mathematical organizations Conferences : Links to conferences about or related to geometric group theory Publications : Journals, publishers, and preprint servers of interest to members of the field Resources : Problem lists, software systems, and miscellaneous links related to geometric group theory Home People Organizations Conferences ... Resources Please send comments about this page to Jon McCammond at jon.mccammond(at)math.ucsb.edu Last Modified on 20/May/04

8. Group Theory The development of group theory. The three main areas that were to give riseto group theory are geometry at the beginning of the 19 th Century,; http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Development_group_theory.htm

The development of group theory Algebra index History Topics Index The study of the development of a concept such as that of a group has certain difficulties. It would be wrong to say that since the non-zero rationals form a group under multiplication then the origin of the group concept must go back to the beginnings of mathematics. Rather we must take the view that group theory is the abstraction of ideas that were common to a number of major areas which were being studied essentially simultaneously. The three main areas that were to give rise to group theory are:- geometry at the beginning of the 19 th Century, number theory at the end of the 18 th Century, the theory of algebraic equations at the end of the 18 th Century leading to the study of permutations. (1) Geometry has been studied for a very long time so it is reasonable to ask what happened to geometry at the beginning of the 19 th Century that was to contribute to the rise of the group concept. Geometry had began to lose its 'metric' character with projective and non-euclidean geometries being studied. Also the movement to study geometry in n dimensions led to an abstraction in geometry itself. The difference between metric and incidence geometry comes from the work of Monge , his student Carnot and perhaps most importantly the work of Poncelet . Non-euclidean geometry was studied by Lambert Gauss Lobachevsky Bolyai among others.

9. Group Theory The development of group theory. Algebra index. History Topics Index. The study of the development of a concept such as that of a group has certain difficulties. Rather we must take the view that http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Development_group_theory.

The development of group theory Algebra index History Topics Index The study of the development of a concept such as that of a group has certain difficulties. It would be wrong to say that since the non-zero rationals form a group under multiplication then the origin of the group concept must go back to the beginnings of mathematics. Rather we must take the view that group theory is the abstraction of ideas that were common to a number of major areas which were being studied essentially simultaneously. The three main areas that were to give rise to group theory are:- geometry at the beginning of the 19 th Century, number theory at the end of the 18 th Century, the theory of algebraic equations at the end of the 18 th Century leading to the study of permutations. (1) Geometry has been studied for a very long time so it is reasonable to ask what happened to geometry at the beginning of the 19 th Century that was to contribute to the rise of the group concept. Geometry had began to lose its 'metric' character with projective and non-euclidean geometries being studied. Also the movement to study geometry in n dimensions led to an abstraction in geometry itself. The difference between metric and incidence geometry comes from the work of Monge , his student Carnot and perhaps most importantly the work of Poncelet . Non-euclidean geometry was studied by Lambert Gauss Lobachevsky Bolyai among others.

10. An Introduction To GROUP THEORY What is group theory? What is the operation symbolized by the dot (•)? group theoryis concerned with systems in which (2) always has a unique solution. http://members.tripod.com/~dogschool/groups.html

var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" What is GROUP THEORY? We'll throw some light on the title question of this page by asking another question. What is the solution of the equation The answer depends on what "things" we allow x to be. If we are doing all our arithmetic using the integers then there is no solutionthere is no integer that gives 3 upon being multiplied by 4. On the other hand if we are doing our arithmetic in Z /5 ("Integers mod 5" as it's sometimes called) then x = 2 is a solution. If we are using the more usual rational number system Q , then the solution is x We can gain insight into all such questions by considering the equation and then bringing up the question of solutions. Well, what objects are a and b ? To what class of objects is x Group theory is concerned with systems in which (2) always has a unique solution. The theory does not concern itself with what a and b The axioms (basic rules) for a group are: CLOSURE : If a and b are in the group then is also in the group.

11. Group Theory From MathWorld group theory from MathWorld The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/GroupTheory.html&a

12. People In Geometric Group Theory People in Geometric group theory. The following is a list of scholarsin geometric group theory and lowdimensional topology (and http://www.math.ucsb.edu/~jon.mccammond/geogrouptheory/people.html

Home People Organizations Conferences ... Resources People in Geometric Group Theory The following is a list of scholars in geometric group theory and low-dimensional topology (and a few members of neighboring fields), with links to their web pages. Please notify me of errors or omissions. Subject Area Lists: Group Theory Magnus Topology Geometry-Topology ... Combinatorics General Lists: Mathematicians with homepages Combined Membership List Other Mathematicians Individuals A B C D ... Z Herbert Abels of U. Bielefeld, Germany Peter Abramenko of U. Virginia Colin Adams of Williams C. Scott Adams of U. Minnesota Ian Agol of U. Illinois - Chicago Emina Alibegovic of U. Michigan Daniel Allcock of U. Texas - Austin B.J.T. Allenby of U. Leeds, U.K. Elizabeth Allman of U. N. Carolina - Asheville Roger Alperin of San Jose State U. Joe Altobelli of Kent State Fredric Ancel of U. Wisconsin - Milwaukee Jim Anderson of U. Southampton, U.K. David Bachman of Cal Poly Patrick Bahls of U. Illinois - Urbana-Champaign Werner Ballmann of U. Bonn, Germany

13. MIT LCS Theory Of Computation Group Theory of Computation Group. The Theory of Computation (TOC) Group is part of the MIT Laboratory for Computer Science. http://theory.lcs.mit.edu/

Theory of Computation Group The Theory of Computation (TOC) Group is part of the MIT Laboratory for Computer Science . We're one of the largest theoretical computer science research groups in the world, and we have faculty, students, and visitors from both the Department of Electrical Engineering and Computer Science and the Department of Mathematics Research Groups Algorithms Computation and Biology Distributed Systems Semantics ... People Events Theory of Computation (TOC) Seminars TOC Student Seminars EECS link to other seminars of interest Computational Biology Seminars Other resources The TOC FTP area Other TOC Resources Area II Graduate Study Guides Classes 6.042 Mathematics for Computer Science 6.045 Theory of Computation 6.046 Algorithms 6.854 Advanced Algorithms ... 6.875 Crypto Administrivia Administrivia area for Theory Group Faculty webmaster@theory.lcs.mit.edu

14. New York Group Theory Cooperative New York group theory Cooperative. Click here to enter http//zebra.sci.ccny.cuny.edu/web/ Domain Name Registration and Domain http://www.grouptheory.org/

New York Group Theory Cooperative Click here to enter http://zebra.sci.ccny.cuny.edu/web/ mydomain.com - Register your domain name

15. TOPOLOGICAL METHODS IN GROUP THEORY Table of contents only, but draft chapters can be downloaded by arrangement. http://math.binghamton.edu/ross/contents.html

TOPOLOGICAL METHODS IN GROUP THEORY by Ross Geoghegan This book is reasonably near completion. From the Introduction: "This is a book about the interplay between algebraic topology and the theory of infinite discrete groups. I have written it for three kinds of readers. First, it is for graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric and homological group theory. Secondly, I am writing for group theorists who would like to know more about the topological side of their subject but who have been too long away from topology. Thirdly, I hope the book will be useful to manifold topologists, both high- and low-dimensional, as a reference source for basic material on proper homotopy and homology..." TABLE OF CONTENTS (draft chapters can be downloaded by arrangement) CHAPTER 1: CW complexes and cellular homology 1.1 Review of general topology 1.2 CW complexes 1.3 Homotopy 1.4 Maps between CW complexes 1.5 Review of chain complexes

16. Higher Dimensional Group Theory Higher Dimensional group theory. by Ronald Brown. Comments 7 April,2004. It Understanding of some phenomena in group theory. There http://www.bangor.ac.uk/~mas010/hdaweb2.htm

Higher Dimensional Group Theory by Ronald Brown Comments: 7 April, 2004 It is more than time to make some additional comments for these pages, as much has happened in the period since 1999. So much, indeed, that I cannot envisage in the time available a full update of the bibliography. What I can hope to do is point out some trends and give some indications of more recent literature. First of all, the title of this web page has not gained much currency, but a web search on " Higher dimensional algebra " shows that this more general term has caught on. It was introduced in my survey article [B:87] in the words: `A naive viewpoint is that n -dimensional geometry needs n -dimensional algebra'. John Baez has many articles and writings putting over this point of view, more than the three listed in the bibliography here. His web page ` This week's find in mathematical physics ' has many items in this area, and you could start at week 53 from 1995. There is much discussion in the Newsgroup: sci.physics.research. A lot of research in Higher Dimensional Algebra is concerned, for good reasons, with notions of weak infinity category. A good survey of definitions on this is by Tom Leinster, published in TAC . Work on this was stimulated by the 1983 manuscript of Alexander Grothendieck, Pursuing Stacks, which is now being edited for publication by the SMF by

17. New York Group Theory Cooperative Home of the Free Magnus combinatorial group theory software project http://zebra.sci.ccny.cuny.edu/web/

18. Open Problems In Group Theory Open Problems. in combinatorial and geometric group theory. This pagehas been accessed times since 10/16/97. We have collected here http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/

Open Problems in combinatorial and geometric group theory This page has been accessed times since 10/16/97. We have collected here over 150 open problems in combinatorial group theory, and we invite the mathematical community to submit more problems as well as comments, suggestions, and/or criticism. Please send us e-mail at daly@rio.sci.ccny.cuny.edu This collection of problems has been selected by G.Baumslag, A.Miasnikov and V.Shpilrain with the help of several members and friends of the New York Group Theory Cooperative. In particular, we are grateful to G.Bergman G.Conner W.Dicks R.Gilman ... I.Kapovich , V. Remeslennikov, V.Roman'kov E.Ventura and D.Wise for useful comments and discussions. Our policy Hall of Fame We have arranged the problems under the following headings: Outstanding Problems Free groups One-relator groups Finitely presented groups ... Algorithmic problems Periodic groups (under construction) Groujps of matrices Hyperbolic and automatic groups Nilpotent groups Metabelian groups ... Group actions

19. Schur Group Theory Software Schur group theory Software. by Brian G. Wybourne. Wybourne s Home Pagewith lots more about group theory and Schur. Version Schur 5.3.1. http://smc.vnet.net/Schur.html

Schur Group Theory Software by Brian G. Wybourne It is my sad duty to report that Dr. Wybourne passed away recently. He will be very greatly missed. An Interactive Program For Calculating Properties Of Lie Groups and Symmetric Functions Wybourne's Home Page with lots more about Group Theory and Schur Version Schur 5.3.1 Functions to treat non-compact groups. Now over 160 functions. Updated manual - now over 220 pages. Platforms currently supported: Intel-compatible PC's (DOS or DOS Window under Windows 3.1, 95, 98, NT, 2000 ) Sun SPARC (Solaris 2.5-8) Intel-compatible PC's (Solaris 2.6-8) Intel-compatible PC's (Red Hat Linux) We expect to have a Max OS X release soon. Pricing and Ordering For details of pricing and ordering go to Contact Information. What is Schur? Schur is a stand alone C program for interactively calculating properties of Lie groups and symmetric functions. Schur has been designed to answer questions of relevance to a wide range of problems of special interest to chemists, mathematicians and physicists - particularly for persons who need specific knowledge relating to some aspect of Lie groups or symmetric functions and yet do not wish to be encumbered with complex algorithms. The objective of Schur is to supply results with the complexity of the algorithms hidden from view so that the user can effectively use Schur as a scratch pad, obtaining a result and then using that result to derive new results in a fully interactive manner. Schur can be used as a tool for calculating branching rules

20. International Society For Group Theory In Cognitive Science GTCS. International Society for. group theory in Cognitive Science. BB.Society President Michael Leyton (USA). Eloise group theory in Robotics http://www.rci.rutgers.edu/~mleyton/GT.htm

GT-CS International Society for Group Theory in Cognitive Science BB Society President: Michael Leyton (USA) Eloise Carlton (USA), Vladimir Dorodnitsyn (Russia), Roy Eagleson (Canada), Athanassios Economou (USA), Mario Ferraro (Italy), Victor Finn (Russia), Nathaniel Friedman (USA), Ted Goranson (USA), Bill Hammel (USA), Slavik Jablan (Jugoslavia), Vladimir Koptsik (Russia), Joan Lasenby (UK), Yanxi Liu (USA), Guerino Mazzola (Switzerland), Denes Nagy (Japan), Thomas Noll (Germany), Frank Park (Korea), Jean Petitot (France), Vladimir Petrov (Russia), Robin Popplestone (USA), Robert Rosen (Canada), Charles Schmidt (USA), Barry Smith (USA), George Stiny (USA), Alexander Voloshinov (Russia), Dorothy Washburn (USA)

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