共查询到19条相似文献,搜索用时 46 毫秒
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有限群G叫(q)-群,如果G中每个次正规子群均为拟正规子群,群G叫Eq-群,若G中每个子群在G中拟正规或自正规,有限群G叫内Eq-群,如果G本身不是Eq-群,但G的每个真子群是Eq-群,本文确定了Eq-群的结构与内Eq-群的分类. 相似文献
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本文证明了下面主要结果:设G是n-可解群,π是一些素数之集,若对任意p∈∩π(G),(p,n(1-n))=1,则G的π-Hall子群的个数r=k1k2...kt,每ki≡1(modp),某P∈π,且每ki整除G的一个主因子。 相似文献
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超可解群的若干充分条件 总被引:12,自引:1,他引:11
关于有限超可解的研究已有不少结果,本文在苏向盈研究有限群的半正规子群的基础上又得到了一系列新的结果(文中定理2—9),本文还对[1]中定理6的证明进行了改进并得到了重要推论,改进的方法在本文得到了充分应用.文中所说群均为有限群,使用的符号是规范的. 相似文献
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超可解群的若干充分条件 总被引:9,自引:0,他引:9
本文研究了有限群的超可解性问题,利用子群的共轭可换性概念及极小反例法,获得了一个群为超可解的若干充分条件.举例说明了主要结果中的假设条件是不可少的. 相似文献
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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. 相似文献
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Gregory T. Lee Sudarshan K. Sehgal Ernesto Spinelli 《Algebras and Representation Theory》2014,17(5):1597-1601
Let F be a field of characteristic p > 2 and G a nonabelian nilpotent group containing elements of order p. Write F G for the group ring. The conditions under which the unit group ??(F G) is solvable are known, but only a few results have been proved concerning its derived length. It has been established that if G is torsion, the minimum derived length is ?log2(p + 1)?, and this minimum occurs if and only if |G′| = p. In the present note, we show that the same holds if G has elements of infinite order. 相似文献
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We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C C G (F)(h) = 1 for all nonidentity elements h ∈ H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H. 相似文献
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Qiangwei Song 《代数通讯》2013,41(4):1499-1513
For an odd prime p, we classify the finite two-generator p-groups with cyclic derived group. There are eight types of non-isomorphic groups having at most nine parameters. 相似文献
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Alexander Bors 《代数通讯》2013,41(11):4823-4843
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