Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups
arXiv:math/0702431
Abstract
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.
18 pages, 1 figure