A characterization of finite simple groups with abelian Sylow \(2\)-subgroups (Q1331676)

The authors prove the following theorem: Let \(G\) be a finite group and \(F\) a finite nonabelian simple group with abelian Sylow 2-subgroups. Then \(G\) is isomorphic to \(F\) if and only if the set of element orders for \(G\) coincides with that for \(F\). -- In this paper the Ree-groups case has been treated which is the final case of that investigation. The proof uses the classification of finite simple groups with abelian Sylow 2-subgroups.