ON AUTOMORPHISMS AND ENDOMORPHISMS OF CC GROUPS

Authors

  • H.T. Aslanyan Chair of Mathematical Cybernetics, Russian-Armenian University, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2018.52.1.060

Keywords:

endomorphism, inner automorphism, centralizer

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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Published

2018-04-16

How to Cite

Aslanyan, H. (2018). ON AUTOMORPHISMS AND ENDOMORPHISMS OF CC GROUPS. Proceedings of the YSU A: Physical and Mathematical Sciences, 52(1 (245), 60–63. https://doi.org/10.46991/PYSU:A/2018.52.1.060

Issue

Section

Short Communications