具有C1-可补子群的有限群结构分析
谭立辉;乔守红
【期刊名称】《广东工业大学学报》 【年(卷),期】2012(029)003
【摘要】子群H在群G中被称为是c1-可补的(c1-supplemented),如果存在G的子群K使得G=HK且H∩T≤Z∞(G),其中Z∞(G)是G的超中心.本文研究素数幂阶子群的广义可补性对有限群结构的的影响,得到以下主要定理:对于G的任意Sylow p-子群P,如果P有子群D满足1＜|D|＜|P|且P每一个|D|阶及p|D|阶子群在G中均c1-可补,那么G超可解.该结果推广了一些已知的结果.%A subgroup H is called c,-supplemented in G if there is a subgroup K such that G = HK and H∩ T≤Z∞ ( G) ,where Z∞ ( G) is the hypercenter of G. It investigates the influence of the C1-supplementation of subgroups on the structure of finite groups. The following results which generalize some related known results are obtained. Main Theorem; For any prime divisor p of ∣G∣ , let P be a Sylow P-subgroup of a group G. Suppose that P has a subgroup D satisfying the condition that 1 < ∣D∣ < ∣ P∣ and each subgroup of P of order ∣D∣ and p ∣D∣ is c,-supplemented in G. Then G is supersolvable. 【总页数】3页(46-48)
【关键词】有限群;c1-可补子群;超可解群 【作者】谭立辉;乔守红
【作者单位】广东工业大学应用数学学院,广东 广州510006;广东工业大学应用
具有C1-可补子群的有限群结构分析
