GROUPS WITH SOME CENTRAL AUTOMORPHISMS FIXING THE CENTRAL KERNEL QUOTIENT

Let G be a group. An automorphism α of the group G is called a central automorphism, if x−1x α ∈ Z(G) for all x ∈ G. Let Lc(G) be the central kernel of G, that is, the set of elements of G fixed by all central automorphisms of G and AutLc (G) denote the group of all central automorphisms of G fixing G/Lc(G) element-wise. In the present paper, we investigate the properties of such automorphisms. Moreover, a full classification of p-groups G of order at most p 5 where AutLc (G) = Inn(G) is also given.