Finite p-groups of class ۲ in which each central automorphism is absolute central

Let G be a group and L(G) denotes the absolute center of G, that is the set of elements of G fixed by all automorphisms of G. An automorphism α of G is called an absolute central automorphism if x −۱xα ∈ L(G) for each x ∈ G. Also an automorphism α of G is called a central automorphism if x −۱xα ∈ Z(G) for each x ∈ G. In this paper, we characterize finite p-groups of class ۲ such that every central automorphism is absolute central.

Keywords:

central automorphism , absolute center , finite p-group