Geodesic
On automorphisms and endomorphisms of $CC$ groups
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 1, pp. 60-63

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We consider the question of describing the automorphisms of semigroups $\mathrm{End}(G)$ of groups $G$ having only cyclic centralizers $(CC)$ of nontrivial elements. In particular, we prove that each automorphism of the automorphism group $\mathrm{Aut}(G)$ of groups $G$ from this class is uniquely determined by its action on the elements from the subgroup of inner automorphisms $\mathrm{Inn}(G)$. Note that, for instance, absolutely free groups, free periodic groups of large enough odd periods, $n$-periodic and free products of $CC$ groups also are $CC$ groups. 
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H. T. Aslanyan. On automorphisms and endomorphisms of $CC$ groups. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 1, pp. 60-63. http://geodesic.mathdoc.fr/item/UZERU_2018_52_1_a9/