We give a sufficient condition on a finite p-group G of nilpotency class 2 so that Autc(G) = Inn(G), where Autc(G) and Inn(G) denote the group of all class preserving automorphisms and inner automorphisms of G respectively. Next we prove that if G and H are two isoclinic finite groups (in the sense of P. Hall), then Autc(G) ∼ = Autc(H). Finally we study class preserving automorphisms of groups of order p 5 , p an odd prime and prove that Autc(G) = Inn(G) for all the groups G of order p 5 except two isoclinism families.
Abstract. An automorphism α of a group G is said to be central if α commutes with every inner automorphism of G. We construct a family of non-special finite p-groups having abelian automorphism groups. These groups provide counterexamples to a conjecture of A. Mahalanobis [Israel J. Math., 165 (2008), 161 -187]. We also construct a family of finite p-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].
Let 1 → N → G → H → 1 be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of N and lifting automorphisms of H to certain automorphisms of G.
Abstract. We classify all finite p-groups G for which | Autc(G)| attains its maximum value, where Autc(G) denotes the group of all class preserving automorphisms of G.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.