Centralizer Dimensions of Partially Commutative Metabelian Groups

Centralizer Dimensions of Partially Commutative Metabelian Groups

We establish an upper bound for the centralizer dimension of a partially commutative metabelian group that depends linearly on the number of vertices in a defining graph. It is proved that centralizer dimensions of 2-generated metabelian groups are not bounded above. The exact value of the centraliz...

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Veröffentlicht in:Algebra and logic 2018-03, Vol.57 (1), p.69-80
1. Verfasser: Timoshenko, E. I.
Format: Artikel
Sprache:eng
Schlagworte:
Abelian groups
Algebra
Graph theory
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Upper bounds
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Zusammenfassung:We establish an upper bound for the centralizer dimension of a partially commutative metabelian group that depends linearly on the number of vertices in a defining graph. It is proved that centralizer dimensions of 2-generated metabelian groups are not bounded above. The exact value of the centralizer dimension is computed for a partially commutative metabelian group defined by a cycle.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-018-9479-4