The recognition of finite simple groups with no elements of order 10 by their element orders
The spectrum of a finite group is the set of its element orders. H is said to be a finite cover of G if G is a homomorphic image of H and H is finite. The main aim of this article is to characterize the finite simple groups with no elements of order 10 by its spectrum among covers. At the same time, above simple groups are completely classified. At last, some results on the recognition by spectrum of above groups are also achieved.
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