Automorphisms of Finite Groups

Description

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. Front Matter ....Pages i-xix Preliminaries on p-Groups (Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav)....Pages 1-28 Fundamental Exact Sequence of Wells (Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav)....Pages 29-67 Orders of Automorphism Groups of Finite Groups (Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav)....Pages 69-116 Groups with Divisibility Property-I (Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav)....Pages 117-155 Groups with Divisibility Property-II (Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav)....Pages 157-193 Groups Without Divisibility Property (Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav)....Pages 195-208 Back Matter ....Pages 209-217