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Register a new userOn finite groups with all simple modules of low dimension in characteristic p
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Authors
Geoffrey R. Robinson
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We give a short proof of the fact that if all characteristic p simple modules of the finite group G have dimension less than p, then G has a normal Sylow p-subgroup.
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In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of order $p$, where $p$ is a fixed prime. This measure, known as the $p$-width of $G$, is the minimal $kin mathbb{N}$ such that any $gin G$ can be written as a product of at most $k$ elements of order $p$. Using primarily character theoretic methods, we sharply bound the $p$-width of some low rank families of Lie type groups, as well as the simple alternating and sporadic groups.
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