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Author : William Burnside
Publisher : Unknown
Page : 412 pages
File Size : 51,8 Mb
Release : 1897
Category : Finite groups
ISBN : UCSD:31822035122696
Author : J. L. Mennicke
Publisher : Springer
Page : 279 pages
File Size : 52,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540381204
Author : Sergej I. Adian
Publisher : Springer
Page : 0 pages
File Size : 54,8 Mb
Release : 2011-12-16
Category : Mathematics
ISBN : 3642669344
Three years have passed since the publication of the Russian edition of this book, during which time the method described has found new applications. In [26], the author has introduced the concept of the periodic product of two groups. For any two groups G and G without elements of order 2 and for any 1 2 odd n ~ 665, a group G @ Gmay be constructed which possesses several in 1 2 teresting properties. In G @ G there are subgroups 6 and 6 isomorphic to 1 2 1 2 G and G respectively, such that 6 and 6 generate G @ G and intersect 1 2 1 2 1 2 in the identity. This operation "@" is commutative, associative and satisfies Mal'cev's postulate (see [27], p. 474), i.e., it has a certain hereditary property for subgroups. For any element x which is not conjugate to an element of either 6 1 or 6 , the relation xn = 1 holds in G @ G • From this it follows that when 2 1 2 G and G are periodic groups of exponent n, so is G @ G • In addition, if G 1 2 1 2 1 and G are free periodic groups of exponent n the group G @ G is also free 2 1 2 periodic with rank equal to the sum of the ranks of G and G • I believe that groups 1 2
Author : William Burnside
Publisher : Unknown
Page : 818 pages
File Size : 54,5 Mb
Release : 2004
Category : Burnside problem
ISBN : 0198505868
William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deep twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material.
Author : Moges Mekonnen Shalla , Necati Olgun
Publisher : Infinite Study
Page : 26 pages
File Size : 43,7 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 8210379456XXX
The aim of this article is mainly to discuss the neutrosophic extended triplet (NET) group actions and Burnside’s lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action. Then, we give and proof the Orbit stabilizer formula for NET group by utilizing the notion of NET set theory. Moreover, some results related to NET group action, and Burnside’s lemma are obtained.
Author : Y. Bahturin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 54,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302353
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.
Author : A.I. Kostrikin
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743245
Perhaps it is not inappropriate for me to begin with the comment that this book has been an interesting challenge to the translator. It is most unusual, in a text of this type, in that the style is racy, with many literary allusions and witticisms: not the easiest to translate, but a source of inspiration to continue through material that could daunt by its combinatorial complexity. Moreover, there have been many changes to the text during the translating period, reflecting the ferment that the subject of the restricted Burnside problem is passing through at present. I concur with Professor Kostrikin's "Note in Proof', where he describes the book as fortunate. I would put it slightly differently: its appearance has surely been partly instrumental in inspiring much endeavour, including such things as the paper of A. I. Adian and A. A. Razborov producing the first published recursive upper bound for the order of the universal finite group B(d,p) of prime exponent (the English version contains a different treatment of this result, due to E. I. Zel'manov); M. R. Vaughan-Lee's new approach to the subject; and finally, the crowning achievement of Zel'manov in establishing RBP for all prime-power exponents, thereby (via the classification theorem for finite simple groups and Hall-Higman) settling it for all exponents. The book is encyclopaedic in its coverage of facts and problems on RBP, and will continue to have an important influence in the area.
Author : serge Bouc
Publisher : Springer
Page : 303 pages
File Size : 50,5 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9783642112973
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.
Author : Victor E Hill
Publisher : CRC Press
Page : 264 pages
File Size : 40,9 Mb
Release : 1999-11-22
Category : Mathematics
ISBN : 1584880384
Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters. Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5. The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory. Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.
Author : Francesco Giovanni,Martin Newell
Publisher : Walter de Gruyter GmbH & Co KG
Page : 356 pages
File Size : 44,8 Mb
Release : 2017-03-06
Category : Mathematics
ISBN : 9783110810387
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author : Yakov Berkovich,Zvonimir Janko
Publisher : Walter de Gruyter
Page : 613 pages
File Size : 53,9 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9783110208238
This is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n > 2, (f) two new proofs of Blackburn's theorem on minimal nonmetacyclic groups, (g) classification of p-groups all of whose subgroups of index p2 are abelian, (h) classification of 2-groups all of whose minimal nonabelian subgroups have order 8, (i) p-groups with cyclic subgroups of index p2 are classified. This volume contains hundreds of original exercises (with all difficult exercises being solved) and an extended list of about 700 open problems. The book is based on Volume 1, and it is suitable for researchers and graduate students of mathematics with a modest background on algebra.
Author : Tullio Ceccherini-Silberstein,Michele D'Adderio
Publisher : Springer Nature
Page : 468 pages
File Size : 43,7 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030881092
This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
Author : A.Yu. Ol'shanskii
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401136181
'Ht moi - ..., si favait su comment en reveniT, One service mathematics hal rendered the je n'y serais point aile.' human race. It has put C.
Author : C. M. Campbell,E. F. Robertson,T. C. Hurley,S. J. Tobin,J. J. Ward
Publisher : Cambridge University Press
Page : 321 pages
File Size : 51,9 Mb
Release : 1995-03-16
Category : Mathematics
ISBN : 9780521477505
This two-volume book contains selected papers from the international conference 'Groups 1993 Galway / St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. As with the Proceedings of the earlier 'Groups-St Andrews' conferences it is hoped that the articles in these Proceedings will, with their many references, prove valuable both to experienced researchers and also to new postgraduates interested in group theory.
Author : Tsit-Yuen Lam
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 54,6 Mb
Release : 2001-06-21
Category : Mathematics
ISBN : 0387951830
Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.