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Mat. Zametki, 2015, Volume 97, Issue 2, Pages 286–295 (Mi mz10240)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00084
Ministry of Education and Science of the Russian Federation 2014/138/1052
This work was supported by the Ministry of Education and Science of the Russian Federation (State Assignment no. 2014/138, grant no. 1052) and by the Russian Foundation for Basic Research (grant no. 12-01-00084).


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

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