On recognition of all finite nonabelian simple groups with orders having prime divisors at most 13

Abstract

The spectrum of a group is the set of its element orders. We say that the problem of recognition by spectrum is solved for a finite group if we know the number of pairwise nonisomorphic finite groups with the same spectrum as the group under study. In this article the problem of recognition by spectrum is completely solved for every finite nonabelian simple group with orders having prime divisors at most 13.