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21.25 (2026)

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(T. Breuer, R. M. Guralnick). Let $G$ be a finite simple group and let $p_1, p_2$ be any (not necessarily distinct) prime divisors of $|G|$. Then can we always find Sylow $p_i$-subgroups $H_i$ such that $G = \langle H_1, H_2 \rangle$?

Contributor: T. C. Burness

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