关于2－因指数群

ON 2-FACTOR INDEX GROUPS

如果有限群Ｇ的每个极大子群的指数的质因子个数（重因式按重数计算）都小于或等于ｎ，则称Ｇ为ｎ－因指数群。本文用单群分类定理证明了定理设Ｇ为非可解２－因指数群，则Ｃ／Ｓ（Ｇ）同构于下列形式的群之一：Ｎ＿１×Ｎ＿２×…×Ｎ＿ｔ其中Ｎ＿ｉ∈｛Ａ＿５，Ｓ＿５，Ａ＿６，Ｓ＿６，Ａ＿７，Ｓ＿７｝，Ｎ＿１，Ｎ＿２，…，Ｎ＿ｔ两两不同，ｔ＝１，２，３，４，５，６．

Let m be the set of maximal subgroup of group G.G is said to be 2-factor index group if the number of prime divisors of |G:M|is 1 or 2 forevery M∈m.In this paper,we use classication theorem for finite simplegroups to obtain the following theorem:Theorem Let G be a 2-factor index group and not solvable,then G/S(G)is isomorphic to one of the following groups:N_1×N_2×…×N_twhere N_i∈{A)5,S_5,A_6,S_6,A_7,S_7},N_i≠N_j(i≠j),t=1,2,3,4,5,6.