【摘要】 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。更多还原

【Abstract】 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) refers to the set of maximal subgroup step.The author demonstrates this conjecture is tenable to the compound step simple groups < 106 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.更多还原