Automorphisms of Finite Groups
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Beschreibung
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.
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.
Elucidates automorphisms of groups as a fundamental topic of study in group theory Explores various developments on the relationship between orders of finite groups and their automorphism groups Provides a unified account of important group-theoretic advances arising from this study Includes open problems for future work
Autor*in
Inder Bir Singh Passi
Themen in »Automorphisms of Finite Groups«
Automorphism Central automorphism Coclass tree Divisibility Property Group cohomology Schur multiplier Uniform Lie algebra Wells exact sequence Group extension
Stimmen zu »Automorphisms of Finite Groups«
“The book is valuable as a source of results that are less known and are of independent interest. … the book is aimed at researchers in group theory and at graduate students in algebra. Far from being a comprehensive treatise, it is a useful book to have for those interested in studying the relation between a finite group and its automorphism group.” (Marian Deaconescu, zbMATH 1447.20004, 2020)
“The audience for this interesting book includes group theorists and graduate students headed in this direction.” (Michael Berg, MAA Reviews, October 6, 2019)
“It represents a useful reference text for researchers in the area, but easily doubles as a very readable introductory text for graduate students … .” (Andrea Caranti, Mathematical Reviews, August, 2019)
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