Given a construction f on groups, we say that a group G is f-realisable if there is a group H
such that G≅ f (H), and completely f-realisable if there is a group H such that G≅ f (H) and …

Let $ G $ be a finite group. The automorphism $ sigma $ of a group $ G $ is said to be an
absolute central automorphism, if for all $ xin G $, $ x^{-1} x^{sigma} in L (G) $, where $ L (G) …

A group H is said to be autocapable if there exists a group M such that H is isomorphic to the
absolute central factor group M/L (M) of M. In this paper, we first prove that if N is a …

Let G be a group and let L (G) denote the absolute center of G. An automorphism α of G is
called an absolute central automorphism if x− 1 x α∈ L (G) for each x∈ G. An automorphism …

Let G be a finite p-group. Let Var (G) and IA (G) respectively denote the group of all absolute
central and IA-automorphisms of G. We give necessary and sufficient conditions for a finite …

Let G be a finite non-abelian p-group, where p is a prime number, and Aut (G) be the group
of all automorphisms of G. An automorphism α of G is an absolute central automorphism if x< …

The purpose of this paper is to determine L (G), the absolute center of the group G, when G
is a p-group of maximal class. Particularly we find L (G) for metabelian p-groups of maximal …

Let G be a finite p-group and let Aut_l (G) be the group of absolute central automorphisms of
G. In this paper we give necessary and sufficient condition on G such that each absolute …

Let G be a group. An automorphism α of the group G is called a central automorphism, if x<
sup>-1 xα∈ Z (G) for all x∈ G. Let Lc (G) be the central kernel of G, that is, the set of …

ABSOLUTE CENTRAL AUTOMORPHISMS FIXING THE FRATTINI SUBGROUP keywords:
absolute central automorphism; inner automorphism; Frattin Page 1 ABSOLUTE CENTRAL …