王品超.关于有限群两个超可解子群之积的问题[J].数学研究及应用,1993,13(2):279~282
关于有限群两个超可解子群之积的问题
Products of Two Supersolvable Subgroups of a Finite Group
投稿时间:1991-04-16  
DOI:10.3770/j.issn:1000-341X.1993.02.024
中文关键词:  
英文关键词:
基金项目:山东省自然科学基金资助课题.
作者单位
王品超 山东曲阜师范大学数学系 
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中文摘要:
      
英文摘要:
      In this paper, we give some sufficient conditions for products of two supersolvable sub-groups to be supersolvable groups. Our results generalize some known results.Theorem 1 Let G = HK,(|H|,|K|) = 1, Where H and K are two supersolvable sub-groups. If H is commutative with every maximal subgroup of K, and K is commutative with every maximal subgroup of H, then G is supersolvable.Theorem 2 Let G = HK, H ∩ K = 1, H G, and K be quasinormal in H. If H, K are supersolvable, the G is supersolvable.Theorem 3 Let G= HK,(|H|,|K|) = 1,H,K be two supersolvable subgroups. If H is commutative with any Sylow subgroup of K and any maximal subgroup of every sylow subgroup of K, and K is commutative with any sylow subgroup of H and any maximal subgroup of every sylow subgroup of H, then G is supersolvable. Theorem 4 If H,K are two supersolvable subgroups of G, G= HK, G′is nilpotent, H is quasi normal K, and K is quasi normal in H,then G is supersolvable. Theorem 5 If H,K are two supersolvable subgroups of G, G= HK, H′? G,[H,K]? G,[H,K] is nilpotent, H is quasi normal in K, and K is quasi normal in H,then G is supersolvable.
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