On automorphisms and endomorphisms of CC groups (CC-խմբերի ավտոմորֆիզմների և էնդոմորֆիզմների մասին)

Abstract

We consider the automorphisms description question for the semigroups EndG 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.