数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2007年
4期
356-359
,共4页
θ-偶%极大子群%可解群%超可解群
θ-偶%極大子群%可解群%超可解群
θ-우%겁대자군%가해군%초가해군
θ-pairs%maximal subgroup%solvable group:supersolvable group
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.
對于有限群G的極大子群M,令β(G:M)錶示整除|G:M|的素因子箇數,β(G)錶示所有β(G:M)中的最大數.令U(G)為使得β(G:M)=β(G)的極大子群的集閤.通過對這一類極大子群的θ-偶斌予一定條件,得到瞭判斷群G可解、超可解的新結果.
대우유한군G적겁대자군M,령β(G:M)표시정제|G:M|적소인자개수,β(G)표시소유β(G:M)중적최대수.령U(G)위사득β(G:M)=β(G)적겁대자군적집합.통과대저일류겁대자군적θ-우빈여일정조건,득도료판단군G가해、초가해적신결과.
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.
