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A new characterization of sporadic simple groups. (English) Zbl 0851.20011
The following result is announced without proof. If \(G\) is a finite group, \(M\) is a sporadic simple group such that \(|G|= |M|\), \(\pi_e(G)= \pi_e(M)\), then \(G \cong M\), where \(\pi_e(G)\) is the set of orders of all elements of \(G\).

MSC:
20D08 Simple groups: sporadic groups
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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