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Embeddings between partially commutative groups: two counterexamples

Lookup NU author(s): Dr Andrew Duncan

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

Abstract

In this note we give two examples of partially commutative subgroups of partially commutative groups. Our examples are counterexamples to the Extension Graph Conjecture and to the Weakly Chordal Conjecture of Kim and Koberda. On the other hand we extend the class of partially commutativegroups for which it is known that the Extension Graph Conjecture holds, toinclude those with commutation graph containing no induced C_4 or P_3. In the process, some new embeddings of surface groups into partially commutative groups emerge.

Publication metadata

Author(s): Casals-Ruiz M, Duncan A, Kazachkov I

Publication type: Article

Publication status: Published

Journal: Journal of Algebra

Year: 2013

Volume: 390

Pages: 87-99

Print publication date: 14/06/2013

Date deposited: 27/05/2013

ISSN (print): 0021-8693

ISSN (electronic): 1090-266X

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jalgebra.2013.04.036

DOI: 10.1016/j.jalgebra.2013.04.036

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