Journal article

### Deficiency and abelianized deficiency of some virtually free groups

Abstract:

Let $Q_m$ be the HNN extension of $\Z/m \times \Z/m$ where the stable letter conjugates the first factor to the second. We explore small presentations of the groups $\Gamma_{m,n}=Q_m \ast Q_n$. We show that for certain choices of (m,n), for example (2,3), the group $\Gamma_{m,n}$ has a relation gap unless it admits a presentation with at most 3 defining relations, and we establish restrictions on the possible form of such a presentation. We then associate to each (m,n) a 3-complex with 16 cel...

Publication status:
Published

### Access Document

Publisher copy:
10.1017/SO30500410700045X

### Authors

More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Tweedale, M More by this author
Journal:
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Volume:
143
Issue:
2
Pages:
257-264
Publication date:
2006-07-26
DOI:
EISSN:
1469-8064
ISSN:
0305-0041
URN:
uuid:8586f91f-a42c-47b8-9146-5a0b4cc278be
Source identifiers:
19428
Local pid:
pubs:19428
Language:
English
Keywords: