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 Algebra Logika: Year: Volume: Issue: Page: Find

 Algebra Logika, 2020, Volume 59, Number 2, Pages 239–259 (Mi al945)

Automorphisms of partially commutative metabelian groups

E. I. Timoshenkoab

a Novosibirsk State Technical University
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Automorphisms of a partially commutative metabelian group whose defining graph contains no cycles are studied. It is proved that an $IA$-automorphism of such a group is identical if it fixes all hanging and isolated vertices of the graph. The concepts of a factor automorphism and of a matrix automorphism are introduced. It is stated that every factor automorphism is represented as the product of an automorphism of the defining graph and a matrix automorphism.

Keywords: automorphism, partially commutative group, metabelian group.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613

DOI: https://doi.org/10.33048/alglog.2020.59.205

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UDC: 512.5
Revised: 14.07.2020

Citation: E. I. Timoshenko, “Automorphisms of partially commutative metabelian groups”, Algebra Logika, 59:2 (2020), 239–259

Citation in format AMSBIB
\Bibitem{Tim20} \by E.~I.~Timoshenko \paper Automorphisms of partially commutative metabelian groups \jour Algebra Logika \yr 2020 \vol 59 \issue 2 \pages 239--259 \mathnet{http://mi.mathnet.ru/al945} \crossref{https://doi.org/10.33048/alglog.2020.59.205}