ON AUTOMORPHISMS AND ENDOMORPHISMS OF CC GROUPS - Aslanyan, H.T. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2018)
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.
Keywords: endomorphism; inner automorphism; centralizer