Download or read book Twelve Sporadic Groups written by Robert L. Jr. Griess and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.

Download or read book Twelve Sporadic Groups written by Robert L. Jr. Griess and published by Springer Science & Business Media. This book was released on 1998-08-19 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.

Download or read book Geometry of Sporadic Groups Volume 2 Representations and Amalgams written by Aleksandr Anatolievich Ivanov and published by Cambridge University Press. This book was released on 1999 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second in a two-volume set, for researchers into finite groups, geometry and algebraic combinatorics.

Download or read book Twelve Sporadic Groups written by Robert L. Jr. Griess and published by . This book was released on 2014-01-15 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Finite Simple Groups written by Robert Wilson and published by Springer Science & Business Media. This book was released on 2009-12-12 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].

Download or read book The Monster Group and Majorana Involutions written by Aleksandr Anatolievich Ivanov and published by Cambridge University Press. This book was released on 2009-03-19 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.

Download or read book The Fourth Janko Group written by Alexander A. Ivanov and published by Clarendon Press. This book was released on 2004-11-04 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory and local analysis are combined to construct one of the last of the sporadic finite simple groups - the fourth Janko group J_4. Aimed at graduates and researchers in group theory, geometry and algebra, Ivanov's approach is based on analysis of group amalgams and the geometry of the complexes of these amalgams with emphasis on the underlying theory. An indispensible resource, this book will be a unique and essential reference for researchers in the area. The author is a leading researcher in the field.

Download or read book Symmetry and the Monster written by Mark Ronan and published by Oxford University Press. This book was released on 2007-07-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an exciting, fast-paced historical narrative ranging across two centuries, Ronan takes readers on an exhilarating tour of this final mathematical quest to understand symmetry.

Download or read book The Classification of Finite Simple Groups written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2011 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.

Download or read book Quilts Central Extensions Braid Actions and Finite Groups written by Tim Hsu and published by Springer. This book was released on 2007-05-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quilts are 2-complexes used to analyze actions and subgroups of the 3-string braid group and similar groups. This monograph establishes the fundamentals of quilts and discusses connections with central extensions, braid actions, and finite groups. Most results have not previously appeared in a widely available form, and many results appear in print for the first time. This monograph is accessible to graduate students, as a substantial amount of background material is included. The methods and results may be relevant to researchers interested in infinite groups, moonshine, central extensions, triangle groups, dessins d'enfants, and monodromy actions of braid groups.

Download or read book Recent Developments in Lie Algebras Groups and Representation Theory written by Kailash C. Misra and published by American Mathematical Soc.. This book was released on 2012 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.

Download or read book Algebra Logic And Combinatorics written by Shaun Bullett and published by World Scientific. This book was released on 2016-04-21 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Download or read book The Classification of the Finite Simple Groups Number 3 written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 1994 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR

Download or read book Applying the Classification of Finite Simple Groups written by Stephen D. Smith and published by American Mathematical Soc.. This book was released on 2018-04-30 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.

Download or read book Blocks of Finite Groups written by Luis Puig and published by Springer Science & Business Media. This book was released on 2002-06-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block. But the main discovery of Brauer is perhaps the existence of families of infinitely many nonisomorphic groups having a "common block"; i.e., blocks having mutually isomorphic "source algebras". In this book, based on a course given by the author at Wuhan University in 1999, all the concepts mentioned are introduced, and all the proofs are developed completely. Its main purpose is the proof of the existence and the uniqueness of the "hyperfocal subalgebra" in the source algebra. This result seems fundamental in block theory; for instance, the structure of the source algebra of a nilpotent block, an important fact in block theory, can be obtained as a corollary. The exceptional layout of this bilingual edition featuring 2 columns per page (one English, one Chinese) sharing the displayed mathematical formulas is the joint achievement of the author and A. Arabia.

Download or read book Algebra written by Ernest Shult and published by Springer. This book was released on 2015-07-14 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

Download or read book Regular Subgroups of Primitive Permutation Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.