Growth of products of subsets in finite simple groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912056003788800 |
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| author | Dona, Daniele Maróti, Attila Pyber, László |
| author_facet | Dona, Daniele Maróti, Attila Pyber, László |
| contents | We prove that the product of a subset and a normal subset inside any finite simple non-abelian group $G$ grows rapidly. More precisely, if $A$ and $B$ are two subsets with $B$ normal and neither of them is too large inside $G$, then $|AB| \geq |A||B|^{1-ε}$ where $ε>0$ can be taken arbitrarily small. This is a somewhat surprising strengthening of a theorem of Liebeck, Schul, Shalev. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12128 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth of products of subsets in finite simple groups Dona, Daniele Maróti, Attila Pyber, László Group Theory 20D06, 20F69 We prove that the product of a subset and a normal subset inside any finite simple non-abelian group $G$ grows rapidly. More precisely, if $A$ and $B$ are two subsets with $B$ normal and neither of them is too large inside $G$, then $|AB| \geq |A||B|^{1-ε}$ where $ε>0$ can be taken arbitrarily small. This is a somewhat surprising strengthening of a theorem of Liebeck, Schul, Shalev. |
| title | Growth of products of subsets in finite simple groups |
| topic | Group Theory 20D06, 20F69 |
| url | https://arxiv.org/abs/2401.12128 |