2018; Physical and Mathematical Sciences, 52(1 (245): 60–63
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ON AUTOMORPHISMS AND ENDOMORPHISMS OF CC GROUPS

Hayk Aslanyan*

Received: 2025-02-04 · Published: 2018-04-16

© 2018 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON AUTOMORPHISMS AND ENDOMORPHISMS OF CC GROUPS
Author
Hayk Aslanyan
Published
2018-04-16
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2018.52.1.060

Abstract

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.
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