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On Strictly -Closed Groups

作　　者：何梅[1] 张新建[1] 

机构地区：[1]淮阴师范学院数学系,江苏淮安223300

出　　处：《淮阴师范学院学报（自然科学版）》2004年第3期189-191,共3页Journal of Huaiyin Teachers College;Natural Science Edition

摘　　要：设p为一素数,群G称为强p 闭群,如果G之子群Gp正规于G且商群G／Gp又是幂指数整除p 1的交换群.讨论了强p 闭群的性质并且得到了以下定理.若群G为强p 闭群,则如果p∈π(G),那么p为π(G)的最大素因子,如果p π(G),那么p>q( q∈π(G));如果G／Φp为强p 闭群,则Gp G且G／Gp是幂指数整除p 1的群;G是强p 闭群充要条件是G／Φp是强p 闭群且G′是p 群.Let p be a prime, A group G is said to be strictly p-closed whenever G_p, a Sylow p-subgroup of G, is normal in G with G/G_p abelian of exponent dividing p-1. In this paper, the authors discuss the strictly p-closed groups and get the following theorems: If a group G is a strictly p-closed group and p∈π(G),then p is the largest prime of π(G). If a group G is a strictly p-closed group and pπ(G), then p>q(q∈π(G)); If a group G is a strictly p-closed group, then G_pG and G/G_p is a group of exponent dividing p-1. A group G is a strictly p-closed group if and only if G/G_p is a strictly p-closed group and G′ is a p-subgroup.

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分 类 号：O152.1[理学—数学]