AI 中文总结
该研究证明了有界秩有限单群G(p)（p为素数）的一致扩张性，将例外素数限制在小类，确定了素数幂q下例外集的零维性质，并推广至半单与完全代数群。
AI 中文摘要
我们证明，有界秩且p为素数的有限单群G(p)具有一致扩张性，即所有Cayley图构成（双侧）扩张子族，仅当p属于一小类特殊素数时可能例外。此外，对所有素数幂q，G(q)一致扩张性的可能例外集被证明具有“零维”。我们还将这些结果推广到半单和完全代数群。
英文摘要
We prove that finite simple groups $G(p)$ of bounded rank and with $p$ prime have uniform expansion, that is, the family of all the Cayley graphs forms a family of (two-sided) expanders, except perhaps when $p$ belongs to a small family of exceptional primes. Furthermore, for all prime powers $q$, the set of possible exceptions to uniform expansion of $G(q)$ is shown to have ``dimension zero''. We also extend these results to semisimple and perfect algebraic groups.
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