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This article is cited in 1 scientific paper (total in 1 paper)
On a Presentation of the Automorphism Group of a Partially Commutative Metabelian Group
E. I. Timoshenko Novosibirsk State Technical University
Abstract:
Automorphisms of a partially commutative metabelian group $S_\Gamma$ defined by a finite simple graph $\Gamma$ with $r$ vertices are considered. The monoid $\mathcal P$ of matrices of order $r$ is equipped with a congruence $\approx$. It is proved that the group of automorphisms acting identically on the quotient group by the commutator subgroup $S_\Gamma/[S_\Gamma, S_\Gamma]$ is isomorphic to the quotient monoid $\mathcal P/\approx$.
Keywords:
partially commutative metabelian group, simple graph, monoid, automorphism group.
DOI:
https://doi.org/10.4213/mzm10240
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English version:
Mathematical Notes, 2015, 97:2, 275–283
Bibliographic databases:
UDC:
512.5 Received: 03.01.2013 Revised: 16.10.2013
Citation:
E. I. Timoshenko, “On a Presentation of the Automorphism Group of a Partially Commutative Metabelian Group”, Mat. Zametki, 97:2 (2015), 286–295; Math. Notes, 97:2 (2015), 275–283
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz10240https://doi.org/10.4213/mzm10240 http://mi.mathnet.ru/eng/mz/v97/i2/p286
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This publication is cited in the following articles:
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E. I. Timoshenko, “Avtomorfizmy chastichno kommutativnykh metabelevykh grupp”, Algebra i logika, 59:2 (2020), 239–259
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