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On Primitive and Inner Endomorphisms of Groups

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Abstract

We consider the semigroup \({\cal P}(G)\) of primitive endomorphisms with respect to a free group G for which the group Aut(G) coincides with the group of tame automorphisms TAut(G). We find the necessary and sufficient conditions for a given automorphism to belong to \({\cal P}(G)\) and also the necessary and sufficient conditions for the coincidence of \({\cal P}(G)\) and Aut(G). Considering a free metabelian group G, we prove the quasi-identity \(\varphi \psi \in {\cal P}(G) \Rightarrow \psi \in {\cal P}(G).\). Some properties of inner endomorphisms of metabelian groups are established, and a few corollaries is obtained.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    E. I. Timoshenko

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  1. E. I. Timoshenko
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Correspondence to E. I. Timoshenko.

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 418–428.

The author was supported by the Russian Foundation for Basic Research (Grant 18-01-00100).

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Timoshenko, E.I. On Primitive and Inner Endomorphisms of Groups. Sib Math J 61, 330–337 (2020). https://doi.org/10.1134/S0037446620020159

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  • DOI: https://doi.org/10.1134/S0037446620020159

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