03811nam 22006255 450 991030966260332120200703123334.0981-13-2895-110.1007/978-981-13-2895-4(CKB)4100000007463608(MiAaPQ)EBC5632927(DE-He213)978-981-13-2895-4(PPN)233796088(EXLCZ)99410000000746360820190112d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAutomorphisms of Finite Groups[electronic resource] /by Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav1st ed. 2018.Singapore :Springer Singapore :Imprint: Springer,2018.1 online resource (231 pages)Springer Monographs in Mathematics,1439-7382981-13-2894-3 Introduction -- p-groups -- Fundamental exact sequence of Wells -- Automorphism groups of finite groups -- Groups with Divisibility Property-I -- Groups with Divisibility Property-II -- Groups without Divisibility Property.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.Springer Monographs in Mathematics,1439-7382Group theoryTopological groupsLie groupsFunctions of complex variablesNumber theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Several Complex Variables and Analytic Spaceshttps://scigraph.springernature.com/ontologies/product-market-codes/M12198Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Group theory.Topological groups.Lie groups.Functions of complex variables.Number theory.Group Theory and Generalizations.Topological Groups, Lie Groups.Several Complex Variables and Analytic Spaces.Number Theory.512.2Passi Inder Bir Singhauthttp://id.loc.gov/vocabulary/relators/aut58117Singh Mahenderauthttp://id.loc.gov/vocabulary/relators/autYadav Manoj Kumarauthttp://id.loc.gov/vocabulary/relators/autBOOK9910309662603321Automorphisms of Finite Groups1982515UNINA