Finite Groups With Fixed Point Free Automorphisms Of Prime Order
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A Proof that Finite Groups with a Fixed-point-free Automorphism of Prime Order are Nilpotent
Author | : John Griggs Thompson |
Publisher | : |
Total Pages | : 98 |
Release | : 1959 |
Genre | : Group theory |
ISBN | : |
Nilpotent Groups and their Automorphisms
Author | : Evgenii I. Khukhro |
Publisher | : Walter de Gruyter |
Total Pages | : 269 |
Release | : 2011-04-20 |
Genre | : Mathematics |
ISBN | : 3110846217 |
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
Automorphisms of Finite Groups
Author | : Inder Bir Singh Passi |
Publisher | : Springer |
Total Pages | : 217 |
Release | : 2019-01-12 |
Genre | : Mathematics |
ISBN | : 9811328951 |
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.
A Course in the Theory of Groups
Author | : Derek J.S. Robinson |
Publisher | : Springer Science & Business Media |
Total Pages | : 518 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1441985948 |
"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