有限群的极小子群数与素因子数

The Numbers of Minimum Subgroups and Prime Factors of Finite Group

极小子群是一类特殊的子群,在有限群结构的研究中起重要作用。有限群的极小子群的数量性质能够反映该群的许多性质。文章从极小子群的角度讨论群,并通过对不同性质的有限群进行讨论,给出了其极小子群数与素因子数的关系。

Minimum subgroup is a kind of special subgroup and plays a important role in the study of finite group struc-ture. The number and properties of minimum subgroup of finite group can reflect many properties of this group. From the per-spective of minimum subgroup, the finite groups with different properties are discussed, and then the relation of minimumsubgroups number and prime factors number is obtained.