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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2018, Volume 52, Issue 1, Pages 60–63
(Mi uzeru459)
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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.
Received: 05.02.2018 Accepted: 02.03.2018
Citation:
H. T. Aslanyan, “On automorphisms and endomorphisms of $CC$ groups”, Proceedings of the YSU, Physical and Mathematical Sciences, 52:1 (2018), 60–63
Linking options:
https://www.mathnet.ru/eng/uzeru459 https://www.mathnet.ru/eng/uzeru/v52/i1/p60
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Abstract page: | 119 | Full-text PDF : | 20 | References: | 14 |
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