Journal article

### Embeddings between partially commutative groups: two counterexamples

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.
Publication status:
Published

### Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
JOURNAL OF ALGEBRA
Volume:
390
Pages:
87-99
Publication date:
2013-06-13
DOI:
EISSN:
1090-266X
ISSN:
0021-8693
Source identifiers:
356576
Language:
English
Keywords:
Pubs id:
pubs:356576
UUID:
uuid:f629779e-ac10-425d-8ca9-2a08cf85b7cc
Local pid:
pubs:356576
Deposit date:
2013-11-16