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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
##### Keywords:
orders of elements; finite group; sporadic simple group