Journal article
Linear Diophantine equations and conjugator length in 2-step nilpotent groups
- Abstract:
- We establish upper bounds on the lengths of minimal conjugators in 2-step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp. This enables us to construct a family of finitely generated 2-step nilpotent groups (Gm)m∈N such that the conjugator length function of Gm grows like a polynomial of degree m + 1.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 175.0KB, Terms of use)
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- Publisher copy:
- 10.1112/blms.70327
Authors
+ U.S. National Science Foundation
More from this funder
- Funder identifier:
- https://ror.org/021nxhr62
- Funding agency for:
- Riley, TR
- Grant:
- NSF GCR-2428489
- Publisher:
- Wiley
- Journal:
- Bulletin of the London Mathematical Society More from this journal
- Volume:
- 58
- Issue:
- 3
- Article number:
- e70327
- Publication date:
- 2026-03-09
- Acceptance date:
- 2026-01-25
- DOI:
- EISSN:
-
1469-2120
- ISSN:
-
0024-6093
- Language:
-
English
- Keywords:
- Pubs id:
-
2370653
- Local pid:
-
pubs:2370653
- Deposit date:
-
2026-02-12
- ARK identifier:
Terms of use
- Copyright holder:
- Bridson and Riley
- Copyright date:
- 2026
- Rights statement:
- © 2026 The Author(s). Bulletin of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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