ON AUTOMORPHISMS AND ENDOMORPHISMS OF CC GROUPS

Abstract

We consider the automorphisms description question for the semigroups End($G$) of a group $G$ having only cyclic centralizers (CC) of nontrivial elements. In particular, we prove that each member of the automorphism group Aut($G$) of a group $G$ from this class is uniquely determined by its action on the elements from the subgroup of inner automorphisms Inn($G$). Note that, typical examples of CC groups are absolutely free groups, free periodic groups of large enough odd periods, $n$-periodic and free products of CC groups.