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.