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 Proceedings of the YSU, Physics & Mathematics, 2018, Volume 52, Issue 1, Pages 60–63 (Mi uzeru459)

Communications
Mathematics

On automorphisms and endomorphisms of $CC$ groups

H. T. Aslanyan

Chair of Mathematical Cybernetics RAU, Armenia

Abstract: 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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Document Type: Article
MSC: Primary 20F28; Secondary 20E36, 20D45
Language: English

Citation: H. T. Aslanyan, “On automorphisms and endomorphisms of $CC$ groups”, Proceedings of the YSU, Physics & Mathematics, 52:1 (2018), 60–63

Citation in format AMSBIB
\Bibitem{Asl18} \by H.~T.~Aslanyan \paper On automorphisms and endomorphisms of $CC$ groups \jour Proceedings of the YSU, Physics {\&} Mathematics \yr 2018 \vol 52 \issue 1 \pages 60--63 \mathnet{http://mi.mathnet.ru/uzeru459}