A characterization of some finite simple groups by orders of their solvable subgroups

Abstract

A brand new way to characterize a finite simple group is discovered.Some infinite sequences of non abelian simple groups have turned out to be determined just by each set of orders of solvable subgroups.The set of orders of solvable subgroups of the alternating group A_{5} of degree 5 is {1, 2, 3, 4, 5, 6, 10, 12}.But it is not very easy to see that no other non abelian simple group has such a set as above.In this paper we will study the problem above for any finite simple group.