指数为π-数的极大子群的交(英文)

The Intersection of Maximal Subgroups with Index a π-number

对任意群G,Frat(G)是指G的极大子群的交.研究指数为π-数的极大子群的交,即πFrat(G),得到与Frat(G)类似的性质.

For any group G, the Frattini subgroup Frat（G） is the intersection of all the maximal subgroups of G. In this paper we investigate the characteristic subgroup, πFrat（G） , which is defined as the intersection of all the maximal subgroups with index a π-number. The properties of πFrat（G） are studied and results analogous to those of the Frattini subgroup are established.