关于一类极大子群的θ-偶

摘要

对于有限群G的极大子群M,令β(G:M)表示整除|G:M|的素因子个数,β(G)表示所有β(G:M)中的最大数.令U(G)为使得β(G:M)=β(G)的极大子群的集合.通过对这一类极大子群的θ-偶斌予一定条件,得到了判断群G可解、超可解的新结果.%For a maximal subgroup M of a finite group G,let β(G:M) be the number of primes dividing |G:M| and β(G) be the largest member of all β(G:M).Let U(G)denote the class of maximal subgroups M of G with β(G:M)=β(G).By means of the θ-pairs for the maximal subgroups M ∈U(G),we obtain in this paper some results which imply G to be solvable or supersolvable.