两类有限单群的刻划

The Description of two Categories of Finite Simple Group

文[1]中提出了仅用群的"极大子群阶之集"来刻划有限复阶单群的猜想:"设G是有限群,M是有限复阶单群,则G■M"当且仅当πs(G)=πs(M).这里πs(G)表示G的极大子群阶之集。"并证明了这个猜想对M为阶小于106的复阶单群是成立的。这里对两类有限单群Suzuki无穷系列单群与Mathieu群Mi(i=11,12,22,23,24)证明上述猜想是正确的,即用群的"极大子群阶之集"来刻划两类有限单群。

Abstract：In the first reference, the author conjectures to depict the finite compound step simple group with the set of maximal subgroup step： if G is a limited group and M is a finite compound step simple group, so G≌M, if and only if , ∏s （G）=∏s（M）, here∏s （G） refersto the set of maximal subgroup step. The author demonstrates this conjecture is tenable to the compound step simple groups 〈10^6 with M as their step. The proof of the two finite simple groups Suzuki infinite series simple group and Mathieu group （M1, （i=11,12,22, 23,24））shows that the above conjecture is correct, when depicting two categories of finite simple group with the set of maximal subgroup step.