Superlocals in Symmetric and Alternating Groups

Abstract

On Aschbacher's definition, a subgroup N of a finite group $G$ is called a $p$-superlocal for a prime $p$ if $N = N_G \left( {O_p \left( N \right)} \right)$. We describe the $p$-superlocals in symmetric and alternating groups, thereby resolving part way Problem 11.3 in the Kourovka Notebook [3].