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.
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Translated from Algebra i Logika, Vol. 59, No. 2, pp. 239-259, March-April, 2020.
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Timoshenko, E.I. Automorphisms of Partially Commutative Metabelian Groups. Algebra Logic 59, 165–179 (2020). https://doi.org/10.1007/s10469-020-09588-7
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DOI: https://doi.org/10.1007/s10469-020-09588-7