Download or read book Finite Groups with Fixed point free Automorphisms of Prime Order written by John Thompson and published by . This book was released on 1959 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Groups Having a Fixed point free Automorphism of Prime Order written by Philip T. Guza and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Groups with Fixed point free Automorphisms of Prime Order written by John Thompson and published by . This book was released on 1959 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Proof that Finite Groups with a Fixed point free Automorphism of Prime Order are Nilpotent written by John Griggs Thompson and published by . This book was released on 1959 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automorphisms of Finite Groups written by Inder Bir Singh Passi and published by Springer. This book was released on 2019-01-12 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Download or read book Nilpotent Groups and their Automorphisms written by Evgenii I. Khukhro and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Download or read book A Course in the Theory of Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM
Download or read book Finite Groups which Admit a Fixed point free Automorphism of Order RST written by P. J.. Rowley and published by . This book was released on 1975 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book P Automorphisms of Finite P Groups written by Evgenii I. Khukhro and published by Cambridge University Press. This book was released on 1998-02-13 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers working in group theory and Lie rings.
Download or read book Finite Groups written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 2007 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Finite and Locally Finite Groups written by B. Hartley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Solvability of Finite Groups Admitting Fixed point free Automorphisms of Order Rs written by Elizabeth Wall Ralston and published by . This book was released on 1970 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Groups Admitting a Fixed point free Automorphism written by Peter J. Rowley and published by . This book was released on 2020 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Groups written by Abraham Adrian Albert and published by American Mathematical Soc.. This book was released on 1959 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On generalized fixed point free automorphisms of finite groups written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study of Fixed point free Automorphisms and Solvable Groups written by Emanuel Psaras and published by . This book was released on 2020 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1903, Ferdinand Georg Frobenius made a conjecture that can be stated as such: let G be a group that emits a fixed-point-free automorphism. Then, G is a solvable group. Throughout the rest of the 20th century many different specific cases of this conjecture have been proved (with the cases putting a restriction on the order of the automorphism). For example, in 1959 John Thompson proved this for all such automorphisms with prime order. Later on in the 70's, Elizabeth Ralston proved this result for autmorphisms with the order being a product of two distinct primes for two primes. Finally in the 90's the full conjecture was accepted as being proven as a consequence of some results in the landmark Classification of Finite Simple Groups. As a result, an attempt at an all-encompassing and unified proof of this conjecture has been largely abandoned by group theorists. For this thesis, we will look at a specific case of this conjecture where the order of the automorphism is 4 (as also done in [5]) and try to give a formal proof whilst introducing the necessary results used as tools in said proof.
Download or read book Groups of Prime Power Order Volume 1 written by Yakov Berkovich and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular p-groups and regularity criteria, (c) p-groups of maximal class and their numerous characterizations, (d) characters of p-groups, (e) p-groups with large Schur multiplier and commutator subgroups, (f) (p‒1)-admissible Hall chains in normal subgroups, (g) powerful p-groups, (h) automorphisms of p-groups, (i) p-groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index. The book is suitable for researchers and graduate students of mathematics with a modest background on algebra. It also contains hundreds of original exercises (with difficult exercises being solved) and a comprehensive list of about 700 open problems.
