Download or read book A Study of the Automorphisms and Chains of a Finite Group written by Albert David Polimeni and published by . This book was released on 1965 with total page 152 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 231 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 A Study of the Stabilizing Automorphisms of a Finite Group written by Bruce Staal and published by . This book was released on 1975 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Solvable Subgroups of the Outer Automorphism Group of a Finite Group written by Nguyen Cao Dam and published by . This book was released on 1972 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 of Automorphisms written by Norman Biggs and published by CUP Archive. This book was released on 1971-10-31 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are notes of lectures given at the University of Southampton, October-December 1969. The lectures were intended for research students working in areas related to the topics discussed, and for mathematicians working in other fields who were interested in hearing a survey of some current problems and their background. The character of the lectures has been retained by the inclusion of occasional 'philosophical' remarks, but the text has been kept free of references as far as possible.
Download or read book Finite groups of automorphisms written by Norman Biggs and published by . This book was released on 1969 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Subgroups of the Automorphism Group of a Finite Abelian Group written by William Lee Hightower and published by . This book was released on 1970 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automorphisms of Finite Groups written by Inder Bir S. Passi and published by . This book was released on 2018 with total page 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 Automorphisms of Finite P groups written by Clive Mortimer Reis and published by . This book was released on 1969 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Automorphisms and Derivations of Associative Rings written by V. Kharchenko and published by Springer Science & Business Media. This book was released on 1991-10-31 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of automorphisms and derivations of associative rings is a direct descendant of the development of classical Galois theory and the theory of invariants. This volume presents a comprehensive overview of the methods and results of that theory, which has been greatly enriched during the last twenty years. Some of the material included appears for the first time. Among the problems discussed in this book are the following: construction of a Galois theory for prime and semiprime rings and its application to domains and free algebras; investigation of the problems of the algebraic dependence of automorphisms and derivations; studies of the fixed rings for finite groups and rings of constants for differential Lie algebras acting on the rings; non-commutative invariants of linear groups; theorems of finite groups acting on modular lattices; actions of Hopf algebras. The monograph is meant for specialists in algebra, but it can also be useful for a wider range of mathematicians. The inclusions in the book of the latest achievements on the structural theory of rings with generalized identities makes it desirable reading for graduate
Download or read book Subgroup Lattices of Groups written by Roland Schmidt and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 589 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 The Maximal Factorizations of the Finite Simple Groups and Their Automorphism Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 1990 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result describes completely the maximal factorizations of all the finite simple groups and their automorphism groups. As a consequence, a classification of the maximal subgroups of the finite alternating and symmetric groups is obtained.
Download or read book Self Similar Groups written by Volodymyr Nekrashevych and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.
Download or read book On the Number of Automorphisms of a Finite Group written by Richard S. Rempel and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
