Applications of p-deficiency and p-largeness
(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:
https://lup.lub.lu.se/record/24de708a-4789-4d44-b432-9ebd14588f3a
- author
- Button, Jack and Thillaisundaram, Anitha LU
- publishing date
- 2011
- 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
- 2024-08-13 15:42:12
@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}}, }