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Parabolic and quasiparabolic subgroups of free partially commutative groups |
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| Authors: | Andrew J. Duncan Ilya V. Kazachkov Vladimir N. Remeslennikov |
| Affiliation: | aSchool of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom;bDepartment of Mathematics and Statistics, University of McGill, 805 Sherbrooke West, Montreal, Quebec, Canada, H3A 2K6;cInstitute of Mathematics, (Siberian Branch of Russian Academy of Science) Pevtsova st. 13, 644099, Omsk, Russia |
| Abstract: | Let Γ 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 Γ, 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. |
| Keywords: | Partially commutative groups Right-angled Artin groups Centraliser lattice |
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