Growth of products of subsets in finite simple groups
| Autor: | Dona, Daniele, Maróti, Attila, Pyber, László |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Bull. Lond. Math. Soc., 56(8):2704--2710, 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/blms.13093 |
| Popis: | 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 $|AB| \geq |A||B|^{1-\epsilon}$ where $\epsilon>0$ can be taken arbitrarily small. This is a somewhat surprising strengthening of a theorem of Liebeck, Schul, Shalev. Comment: 7 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|