Thompson's conjecture for alternating group

Abstract

Let $G$ be a finite group, and let $N(G)$ be the set of sizes of its conjugacy classes. We show that if a finite group $G$ has trivial center and $N(G)$ equals to $N(Al{t}_n)$ or $N(Sy{m}_n)$ for $n\ge 23$, then $G$ has a composition factor isomorphic to an alternating group $Al{t}_k$ such that $k\le n$ and the half-interval $(k,n]$ contains no primes. As a corollary, we prove the Thompson's conjecture for simple alternating groups.

References in corpus (1)

• On Thompson's conjecture for alternating group of large degree