Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups

Details Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups

2007-02-14

arxiv.org/abs/math/0702431v1

Mathematics

Group Theory

18 pages, 1 figure

Scientific paper

Let S be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph S, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

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