【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M(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-偶赋予一定条件,得到了判断群G可解、超可解的新结果.更多还原

【Abstract】 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 M(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∈M(G),we obtain in this paper some results which imply G to be solvable or supersolvable.更多还原