Abstract
Let G be a finite non-abelian p-group of order greater than p4, p an odd prime, such that is cyclic and Z(H) is elementary abelian, where
We prove that the set
of all commuting automorphisms of G forms a subgroup of
if and only if
is abelian. Also, we find the structure of
for a finite 2-group G of almost maximal class with cyclic center Z(G), where
denotes the set of all central automorphisms of G.