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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.
DOI:
https://doi.org/10.33048/alglog.2020.59.205
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UDC:
512.5 Received: 30.08.2019 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}
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http://mi.mathnet.ru/eng/al945 http://mi.mathnet.ru/eng/al/v59/i2/p239
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