- Author
- Jan-Christoph Schlage-Puchta (UGent)
- Organization
- Abstract
- We construct, for d >= 2 and epsilon > 0, a d-generated p-group Gamma which, in an asymptotic sense, behaves almost like a d-generated free pro-p-group. We show that a subgroup of index p(n) needs (d - epsilon)p(n) generators, and that the subgroup growth of Gamma satisfies s(p)(n)(Gamma) > s(p)(n)(F-d(p))(1-epsilon), where F-d(p) is the d-generated free pro-p-group. To do this we introduce a new invariant for finitely-generated groups and study some of its basic properties.
- Keywords
- pro-p-groups, subgroup growth, asymptotic group theory, rank gradient
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1989443
- MLA
- Schlage-Puchta, Jan-Christoph. “A P-Group with Positive Rank Gradient.” JOURNAL OF GROUP THEORY, vol. 15, no. 2, 2012, pp. 261–70, doi:10.1515/JGT.2011.101.
- APA
- Schlage-Puchta, J.-C. (2012). A p-group with positive rank gradient. JOURNAL OF GROUP THEORY, 15(2), 261–270. https://doi.org/10.1515/JGT.2011.101
- Chicago author-date
- Schlage-Puchta, Jan-Christoph. 2012. “A P-Group with Positive Rank Gradient.” JOURNAL OF GROUP THEORY 15 (2): 261–70. https://doi.org/10.1515/JGT.2011.101.
- Chicago author-date (all authors)
- Schlage-Puchta, Jan-Christoph. 2012. “A P-Group with Positive Rank Gradient.” JOURNAL OF GROUP THEORY 15 (2): 261–270. doi:10.1515/JGT.2011.101.
- Vancouver
- 1.Schlage-Puchta J-C. A p-group with positive rank gradient. JOURNAL OF GROUP THEORY. 2012;15(2):261–70.
- IEEE
- [1]J.-C. Schlage-Puchta, “A p-group with positive rank gradient,” JOURNAL OF GROUP THEORY, vol. 15, no. 2, pp. 261–270, 2012.
@article{1989443,
abstract = {{We construct, for d >= 2 and epsilon > 0, a d-generated p-group Gamma which, in an asymptotic sense, behaves almost like a d-generated free pro-p-group. We show that a subgroup of index p(n) needs (d - epsilon)p(n) generators, and that the subgroup growth of Gamma satisfies s(p)(n)(Gamma) > s(p)(n)(F-d(p))(1-epsilon), where F-d(p) is the d-generated free pro-p-group. To do this we introduce a new invariant for finitely-generated groups and study some of its basic properties.}},
author = {{Schlage-Puchta, Jan-Christoph}},
issn = {{1433-5883}},
journal = {{JOURNAL OF GROUP THEORY}},
keywords = {{pro-p-groups,subgroup growth,asymptotic group theory,rank gradient}},
language = {{eng}},
number = {{2}},
pages = {{261--270}},
title = {{A p-group with positive rank gradient}},
url = {{http://doi.org/10.1515/JGT.2011.101}},
volume = {{15}},
year = {{2012}},
}
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