Expanders and growth of normal subsets in finite simple groups of Lie type Full article
| Journal |
Bulletin of the London Mathematical Society
ISSN: 0024-6093 , E-ISSN: 1469-2120 |
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| Output data | Year: 2025, Volume: 57, Number: 11, Pages: 3429–3440 Pages count : 12 DOI: 10.1112/blms.70161 | ||
| Tags | word maps; elements | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
We show that some classical results on expander graphsimply growth results on normal subsets in finite simplegroups. As one application, it is shown that given a non-trivial normal subset of a finite simple group of Lietype of bounded rank, we either have ⧵ {1} ⊆ 2 or| 2| ⩾ | |1+ , for > 0. This improves a result of Gill, Pyber, Short, and Szabó, and partially resolves a questionof Pyber from the Kourovka notebook. We also proposea variant of Gowers’ trick for two subsets, and give appli-cations to products of large subsets in groups of Lie type,improving some results of Larsen, Shalev, and Tiep.
Cite:
Skresanov S.V.
Expanders and growth of normal subsets in finite simple groups of Lie type
Bulletin of the London Mathematical Society. 2025. V.57. N11. P.3429–3440. DOI: 10.1112/blms.70161 WOS Scopus РИНЦ OpenAlex
Expanders and growth of normal subsets in finite simple groups of Lie type
Bulletin of the London Mathematical Society. 2025. V.57. N11. P.3429–3440. DOI: 10.1112/blms.70161 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 11, 2024 |
| Accepted: | Jul 11, 2025 |
| Published online: | Jul 25, 2025 |
| Published print: | Nov 30, 2025 |
Identifiers:
| ≡ Web of science: | WOS:001536654200001 |
| ≡ Scopus: | 2-s2.0-105011978187 |
| ≡ Elibrary: | 84821649 |
| ≡ OpenAlex: | W4412910737 |