Finite Groups Which Admit A Fixed Point Free Automorphism Of Order Rst
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| Author | : Wanida Hemakul |
| Publisher | : World Scientific |
| Total Pages | : 755 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814366307 |
This volume is an outcome of the International Conference on Algebra in celebration of the 70th birthday of Professor Shum Kar-Ping which was held in Gadjah Mada University on 7?10 October 2010. As a consequence of the wide coverage of his research interest and work, it presents 54 research papers, all original and referred, describing the latest research and development, and addressing a variety of issues and methods in semigroups, groups, rings and modules, lattices and Hopf Algebra. The book also provides five well-written expository survey articles which feature the structure of finite groups by A Ballester-Bolinches, R Esteban-Romero, and Yangming Li; new results of Grbner-Shirshov basis by L A Bokut, Yuqun Chen, and K P Shum; polygroups and their properties by B Davvaz; main results on abstract characterizations of algebras of n-place functions obtained in the last 40 years by Wieslaw A Dudek and Valentin S Trokhimenko; Inverse semigroups and their generalizations by X M Ren and K P Shum. Recent work on cones of metrics and combinatorics done by M M Deza et al. is included.
| Author | : B. Hartley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 469 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401103291 |
This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
| Author | : Daniel Gorenstein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 546 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821843427 |
"The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups. The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem. This book would be a valuable companion text for a graduate group theory course."--Publisher's website
| Author | : Marcus du Sautoy |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461213800 |
A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.
| Author | : M. J. Collins |
| Publisher | : Cambridge University Press |
| Total Pages | : 260 |
| Release | : 1990-03-22 |
| Genre | : Mathematics |
| ISBN | : 9780521234405 |
Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates that requires only a basic knowledge of group theory and general algebra. This theme is then expanded in a self-contained account providing an introduction to the application of character theory to the classification of simple groups. The book follows both strands of the theory: the exceptional characteristics of Suzuki and Feit and the block character theory of Brauer and includes refinements of original proofs that have become available as the subject has grown.
| Author | : B. Huppert |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 464 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642679978 |
Und dann erst kommt der "Ab -ge - sa. ng\' da. /3 der nidlt kurz und nicht zu la. ng, From "Die Meistersinger von Nürnberg", Richard Wagner This final volume is concerned with some of the developments of the subject in the 1960's. In attempting to determine the simple groups, the first step was to settle the conjecture of Burnside that groups of odd order are soluble. The proof that this conjecture was correct is much too long and complicated for presentation in this text, but a number of ideas in the early stages of it led to a local theory of finite groups, so me aspects of which are discussed in Chapter X. Much of this discussion is a con tinuation of the theory of the transfer (see Chapter IV), but we also introduce the generalized Fitting subgroup, which played a basic role in characterization theorems, that is, in descriptions of specific groups in terms of group-theoretical properties alone. One of the earliest and most important such characterizations was given for Zassenhaus groups; this is presented in Chapter XI. Characterizations in terms of the centralizer of an involution are of particular importance in view of the theorem of Brauer and Fowler. In Chapter XII, one such theorem is given, in which the Mathieu group 9J'l1l and PSL(3, 3) are characterized
| Author | : |
| Publisher | : |
| Total Pages | : 302 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Hans Kurzweil |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 390 |
| Release | : 2006-03-04 |
| Genre | : Mathematics |
| ISBN | : 0387217681 |
From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews
| Author | : Evgenii I. Khukhro |
| Publisher | : Cambridge University Press |
| Total Pages | : 226 |
| Release | : 1998-02-13 |
| Genre | : Mathematics |
| ISBN | : 052159717X |
Ideal for graduate students and researchers working in group theory and Lie rings.
| Author | : Daniel Gorenstein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 474 |
| Release | : 1974 |
| Genre | : Mathematics |
| ISBN | : 0821818473 |
The object of the memoir is to determine all finite simple (and more generally fusion-simple) groups each of whose 2-subgroups can be generated by at most 4 elements. Using a result of MacWilliams, we obtain as a corollary the classifications of all finite simple groups whose Sylow 2-subgroups do not possess an elementary abelian normal subgroups of order 8. The general introduction provides a fairly detailed outline of the over-all proof of our main classification theorem, including the methods employed. The proof itself is divided into six major parts; and the introductory section of each part gives a description of the principal results to be proved in that part.
