41. Permutation Groups Resources Web-based resources for permutation groups and related areas in group theory and combinatorics. http://www.maths.qmw.ac.uk/~pjc/permgps/

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

Information about: TOPOLOGICAL METHODS IN GROUP THEORY by Ross Geoghegan This book was published by Springer, New York in December 2007 It is Vol. 243 of their series Graduate Texts in Mathematics 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 PART I: ALGEBRAIC TOPOLOGY FOR GROUP THEORY CHAPTER 1: CW COMPLEXES AND HOMOTOPY: 1.1 Review of general topology

43. Group Theory Authors/titles "new.GR" Submissions received from Wed 20 Oct 10 to Thu 21 Oct 10, announced Fri, 22 Oct 10 http://arxiv.org/list/math.GR/new

arXiv.org math math.GR Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Group Theory New submissions Submissions received from Wed 27 Oct 10 to Thu 28 Oct 10, announced Fri, 29 Oct 10 New submissions Cross-lists Replacements [ total of 8 entries: [ showing up to 2000 entries per page: fewer more New submissions for Fri, 29 Oct 10 arXiv:1010.5836 pdf ps other Title: The Structure of Divisible Abelian Groups Authors: Daniel Miller Subjects: Group Theory (math.GR) This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible group is a direct sum of copies of the additive rationals and quasicyclic groups. arXiv:1010.5965 pdf ps other Title: Authors: Madad Khan Faisal Venus Amjid Subjects: Group Theory (math.GR) arXiv:1010.6022 pdf ps other Title: Authors: Comments: 14 pages Subjects: Group Theory (math.GR) arXiv:1010.6043 pdf ps other Title: The fundamental group of random 2-complexes Authors: Eric Babson Christopher Hoffman Matthew Kahle Comments: 26 pages, 3 figures

44. 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. http://www.bath.ac.uk/~masgcs/gpf.html

Group Pub Forum 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 mailing list is a private list. To join it go here

45. An Introduction To GROUP THEORY 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 http://dogschool.tripod.com/groups.html

Build your own FREE website at Tripod.com Share: Facebook Twitter Digg reddit document.write(lycos_ad['leaderboard']); document.write(lycos_ad['leaderboard2']); 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.

46. International Society For Group Theory In Cognitive Science Group theory in Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufacturing, Epistemology, Measurement, Computation, Neuroscience, Anthropology, Semiotics. 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)

47. Group Theory: Definition From Answers.com n. The branch of mathematics concerned with groups and the description of their properties. http://www.answers.com/topic/group-theory

48. Cvitanovic, P.: Group Theory: Birdtracks, Lie's, And Exceptional Groups. of the book Group Theory Birdtracks, Lie's, and Exceptional Groups by Cvitanovic, P., published by Princeton University Press...... http://press.princeton.edu/titles/8839.html

49. GAP System For Computational Discrete Algebra GAP is a free system for computational discrete algebra. http://www.gap-system.org/

@import url(lib/gw.css); GAP Main Branches Download Overview Data Libraries Packages ... Sitemap Navigation Tree Start Download Overview Data Libraries ... GAP 3 Quicklinks Site Structure Search Web Site Capabilities Manuals ... References Welcome to GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra What is GAP? GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory . GAP provides a programming language , a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. See also the overview and the description of the mathematical capabilities . GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely . You can study and easily modify or extend it for your special use. The current release is GAP 4.4.12. The pages of this web site describe this release if not stated otherwise. The webpage

50. World Of Groups Welcome to The World of Groups! This part of the World Wide Algebra project includes a list of open problems in combinatorial group theory, a list of personal web pages, a list http://www.grouptheory.info/

51. Group Theory | SimBio SimBiotic President Eli MeirThere was an interesting news item in the October 9 edition of Nature about applying group theory to scientific authorship by http://simbio.com/content/group-theory

@import "/sites/default/modules/button_style/button_style.css"; @import "/modules/node/node.css"; @import "/modules/system/defaults.css"; @import "/modules/system/system.css"; @import "/modules/user/user.css"; @import "/sites/default/modules/cck/content.css"; @import "/sites/default/modules/lightbox2/css/lightbox.css"; @import "/sites/default/modules/cck/fieldgroup.css"; @import "/sites/default/modules/forward/forward.css"; @import "/modules/comment/comment.css"; @import "/sites/default/themes/simbiotic/style.css"; home products: college products: K-12 order ... contact Group Theory Submitted by Eli_Meir on Fri, 11/07/2008 - 19:55. There was an interesting news item in the October 9 edition of Nature about applying group theory to scientific authorship by John Whitfield . Although it didn't mention this at all, it started me thinking about group sizes in classes. The essay starts by pointing out that scientific studies used to have single authors, but over the last few decades, single author papers have become vanishingly rare (personally I think I've published one, out of around 20 papers, and that one was a review). Apparently there is now a wave of work from several labs looking at the nature of scientific collaborations, as evidenced by authorship on papers, and how productive different kinds of collaborations are. Some of the interesting points: If you team up with someone from another institution (of equal or higher tier to your own), the resulting papers are more highly cited than if you team with someone from your own institution.

52. Permutation Group Problems Compiled by Peter Cameron. http://www.maths.qmw.ac.uk/~pjc/pgprob.html

53. 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 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.

54. Papers By R. E. Borcherds Including proof of the Moonshine Conjecture (TeX, DVI, PDF). http://math.berkeley.edu/~reb/papers/

PDF, dvi and plain TeX files of papers and preprints by R. E. Borcherds tex dvi pdf A monster Lie algebra? (with J. H. Conway , L. Queen and N. J. A. Sloane .) Adv. Math. 53 (1984) 75-79. tex dvi pdf The Leech lattice and other lattices, Ph.D. thesis (Cambridge, 1985). tex dvi pdf The Leech lattice, Proc. Royal Soc. London A398 (1985) 365-376. tex dvi pdf Vertex algebras, Kac-Moody algebras and the monster, Proc.Nat. Acad. Sci. U.S.A. 83 (1986), 3068-3071. tex dvi pdf Automorphism groups of Lorentzian lattices, J.Alg. Vol 111, No. 1, Nov 1987, pp. 133-153. tex dvi pdf Generalized Kac-Moody algebras, J.Alg. Vol 115, No. 2, June 1988, p. 501-512. tex dvi pdf The 24-dimensional odd unimodular lattices. Sphere packings, lattices, and groups, by J.H. Conway and N. J. A. Sloane , chapter 17 (p. 421-430.) (This does not include the table of such lattices, which can be extracted from table -4 of "The Leech lattice and other lattices". ) tex dvi pdf The cellular structure of the Leech lattice. (with J. H. Conway and L. Queen) Sphere packings, lattices, and groups, by J.H. Conway and N. J. A. Sloane

55. Group Theory File Format PDF/Adobe Acrobat http://www.jmilne.org/math/CourseNotes/GT.pdf

56. {group Theory} group theory, inc Bang Pop Shot on location in Philadelphia, PA Director Josh Nussbaum Producer - Ben Nabors http://www.group-theory.net/

Photo by: Carlos Pavan Project: Moving Windmills

57. Trinomials With Interesting Galois Groups Parametrisation of trinomials with Galois groups contained in the simple group G168. http://www.math.harvard.edu/~elkies/trinomial.html

Trinomials ax n bx c with interesting Galois groups In 1969 Trinks discovered that the irreducible trinomial x x factored modulo small primes (other than the primes 3 and 7 dividing its discriminant 21 ), always yielded polynomials of degrees 7, 4+2+1, 3+3+1, or 2+2+1+1+1. [The pattern 1+1+1+1+1+1+1, for complete factorization into linear polynomials, occurs too, but not until we reach 1879, the 289th prime.] This suggested that the trinomial had Galois group G , the simple group of order 168 consisting of the invertible 3-by-3 matrices mod 2, acting on the 7 nonzero vectors in ( Z Z (that is, on the point of the finite projective plane of order 2). Matzat then proved that the Galois group was in fact G . Of course every trinomial equivalent to x x +3 (i.e., proportional to ( mx mx +3 for some nonzero m ) has the same Galois group. Ten years later, Erbach, Fischer and McKay [EFM] published the trinomial x x not equivalent with the Trinks-Matzat trinomial, and showed that it too has Galois group G . In 1999 I analyzed the general problem of trinomials ax bx c with Galois group contained in G . The analysis led me to the new examples x x x x and to the conjecture that every G -trinomial is equivalent to either Trinks-Matzat, Erbach-Fischer-McKay, or one of the two new trinomials. This was proved in 2001 by Nils Bruin. (A copy of the input files of his computations is

58. Group Theory The New York Group Theory Cooperative is an association of group theorists based at The City College of the City University of New York. It is supported, in part, by the Algebra http://www.group-theory.org/

59. GROUP ACTION FORUM Association for the study of the theory of transformation groups and related topics. Members, news, events, publications. http://gaf.astagor.net/

GAF Group Action Forum an international mathematical association

60. The Lie Algebras Su(N) (by Walter Pfeifer) Publication An Introduction to the Lie Algebras su(N). By Walter Pfeifer, Switzerland. A free copy can be ordered. http://lie.walterpfeifer.ch/

Publications in Physics and Mathematics by Walter Pfeifer Order for free Reader's comments Table of Contents Description ... Contact The Lie Algebras su N ), an Introduction 2003 (revised 2008) ISBN 3-7643-2418-X The su N ) Lie algebras very frequently appear and "there is hardly any student of physics or mathematics who will never come across symbols like su ) and su )" (Fuchs, Schweigert, 1997, p. XV). For instance, the algebra su ) describes angular momenta, su ) is related to harmonic oscillator properties or to rotation properties of systems and su ) represents states of elementary particles in the quark model. This book is mainly directed to undergraduate students of physics or to interested physicists. It is conceived to give directly a concrete idea of the su N ) algebras and of their laws. The detailed developments, the numerous references to preceding places, the figures and many explicit calculations of matrices should enable the beginner to follow. Laws which are given without proof are marked clearly and mostly checked with numerical tests. Knowledge of basic linear algebra is a prerequisite. Many results are obtained, which hold generally for (simple) Lie algebras. Therefore, the text on hand can make the lead-in to this field easier. The structure of the contents is simple. First, Lie algebras are defined and the

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