Embeddings between partially commutative groups: two counterexamples

Montserrat Casals-Ruiz; Andrew Duncan; Ilya Kazachkov

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arXiv · 1306.3087

Embeddings between partially commutative groups: two counterexamples

Montserrat Casals-Ruiz·Andrew Duncan·Ilya Kazachkov

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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, \cite{KK}. On the other hand we extend the class of partially commutative groups for which it is known that the Extension Graph Conjecture holds, to include 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.

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Montserrat Casals-Ruiz, Andrew Duncan, Ilya Kazachkov. 2013-06-13. Embeddings between partially commutative groups: two counterexamples. https://arxiv.org/abs/1306.3087

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