Automorphisms of Partially Commutative Metabelian Groups

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 automorph...

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Veröffentlicht in:	Algebra and logic 2020-05, Vol.59 (2), p.165-179
1. Verfasser:	Timoshenko, E. I.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Apexes Automorphisms Graph theory Graphical representations Mathematical Logic and Foundations Mathematics Mathematics and Statistics
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description	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.
doi_str_mv	10.1007/s10469-020-09588-7
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subjects	Algebra Apexes Automorphisms Graph theory Graphical representations Mathematical Logic and Foundations Mathematics Mathematics and Statistics
title	Automorphisms of Partially Commutative Metabelian Groups
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