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We show that small normal subsets A of finite simple groups grow very rapidly – namely, |A| ≥ |A|2− , where > 0 is arbitrarily small. Extensions, consequences, and a… Click to show full abstract
We show that small normal subsets A of finite simple groups grow very rapidly – namely, |A| ≥ |A|2− , where > 0 is arbitrarily small. Extensions, consequences, and a rapid growth result for simple algebraic groups are also given. The first and third authors acknowledge the support of EPSRC Mathematics Platform grant EP/I019111/1. The second and third authors acknowledge the support of an ERC advanced grant 247034 and of an Israel Science Foundation grant 1117/13. The third author acknowledges the support of the Vinik Chair of Mathematics which he holds. 2010 Mathematics Subject Classification: 20D06, 20F69
Journal Title: Transactions of the American Mathematical Society
Year Published: 2017
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