Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Applications of p-deficiency and p-largeness

Button, Jack and Thillaisundaram, Anitha LU (2011) In International Journal of Algebra and Computation 2(4).
Abstract
We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is GolodShafarevich, and has a finite index subgroup which is GolodShafarevich for the remaining primes. We also generalize a result of Grigorchuk on Coxeter groups to odd primes.
Please use this url to cite or link to this publication:
author
and
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal of Algebra and Computation
volume
2
issue
4
publisher
World Scientific Publishing
external identifiers
  • scopus:79959738673
ISSN
0218-1967
DOI
10.1142/S0218196711006339
language
English
LU publication?
no
id
24de708a-4789-4d44-b432-9ebd14588f3a
date added to LUP
2024-06-07 14:36:30
date last changed
2025-04-04 14:29:27
@article{24de708a-4789-4d44-b432-9ebd14588f3a,
  abstract     = {{We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is GolodShafarevich, and has a finite index subgroup which is GolodShafarevich for the remaining primes. We also generalize a result of Grigorchuk on Coxeter groups to odd primes.}},
  author       = {{Button, Jack and Thillaisundaram, Anitha}},
  issn         = {{0218-1967}},
  language     = {{eng}},
  number       = {{4}},
  publisher    = {{World Scientific Publishing}},
  series       = {{International Journal of Algebra and Computation}},
  title        = {{Applications of p-deficiency and p-largeness}},
  url          = {{http://dx.doi.org/10.1142/S0218196711006339}},
  doi          = {{10.1142/S0218196711006339}},
  volume       = {{2}},
  year         = {{2011}},
}