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- W2951843628 abstract "We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If k is the minimal degree of a representation of the finite group G, then for every subset B of G with $|B| > |G| / k^{1/3}$ we have B^3 = G. We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan's theorem which implies that if k>1, then G has a proper subgroup of index at most ck^2 for some absolute constant c, hence a product-free subset of size at least $|G| / c'k$. This answers a question of Gowers." @default.
- W2951843628 created "2019-06-27" @default.
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- W2951843628 date "2007-03-12" @default.
- W2951843628 modified "2023-09-27" @default.
- W2951843628 title "Product decompositions of quasirandom groups and a Jordan type theorem" @default.
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