On Thompson's conjecture for alternating group of large degree

Abstract

For a finite group $G$, let $N(G)$ denote the set of conjugacy class sizes of $G$. We show that if every finite group $G$ with trivial center such that $N(G)$ equals to $N(Al{t}_n)$, where $n>1361$ and at least one of numbers $n$ or $n-1$ are decomposed into a sum of two primes, then $G\simeq Al{t}_n$.

References in corpus (1)

• On finite groups isospectral to simple classical groups

Cited by in corpus (1)

• Thompson's conjecture for alternating group