共查询到20条相似文献,搜索用时 15 毫秒
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I. K. Chirik 《Mathematical Notes》2016,99(1-2):116-119
The solvability of any finite group of the form G = AB is established under the assumption that the subgroups A and B are solvable and KP2-subnormal in the group G. 相似文献
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A subgroup H of a group G is said to be K-?-subnormal in G if H can be joined to the group by a chain of subgroups each of which is either normal in the next subgroup or of prime index in it. Properties of K-?-subnormal subgroups are obtained. A class of finite groups whose Sylow p-subgroups are K-?-subnormal in G for every p in a given set of primes is studied. Some products of K-?-subnormal subgroups are investigated. 相似文献
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Let σ = {σ_i | i ∈ I} be some partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σ_i-subgroup of G, for some i ∈ I, and H contains exactly one Hall σ_i-subgroup of G for every σ_i ∈σ(G). A subgroup H of G is said to be: σ-permutable or σ-quasinormal in G if G possesses a complete Hall σ-set H such that HA~x= A~xH for all A ∈ H and x ∈ G:σ-subnormal in G if there is a subgroup chain A = A_0≤A_1≤···≤ A_t = G such that either A_(i-1)■A_i or A_i/(A_(i-1))A_i is a finite σ_i-group for some σ_i ∈σ for all i = 1,..., t.If M_n M_(n-1) ··· M_1 M_0 = G, where Mi is a maximal subgroup of M_(i-1), i = 1, 2,..., n, then M_n is said to be an n-maximal subgroup of G. If each n-maximal subgroup of G is σ-subnormal(σ-quasinormal,respectively) in G but, in the case n 1, some(n-1)-maximal subgroup is not σ-subnormal(not σ-quasinormal,respectively) in G, we write m_σ(G) = n(m_(σq)(G) = n, respectively).In this paper, we show that the parameters m_σ(G) and m_(σq)(G) make possible to bound the σ-nilpotent length l_σ(G)(see below the definitions of the terms employed), the rank r(G) and the number |π(G)| of all distinct primes dividing the order |G| of a finite soluble group G. We also give the conditions under which a finite group is σ-soluble or σ-nilpotent, and describe the structure of a finite soluble group G in the case when m_σ(G) = |π(G)|. Some known results are generalized. 相似文献
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A subgroup H of a finite group G is called ℙ-subnormal in G whenever H either coincides with G or is connected to G by a chain of subgroups of prime indices. If every Sylow subgroup of G is ℙ-subnormal in G then G is called a w-supersoluble group. We obtain some properties of ℙ-subnormal subgroups and the groups that are products of two ℙ-subnormal subgroups, in particular,
of ℙ-subnormal w-supersoluble subgroups. 相似文献
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Let ? be a subgroup-closed saturated formation. A finite group G is called an ?pc-group provided that each subgroup X of G is ?-subabnormal in the ?-subnormal closure of X in G. Let ?pc be the class of all ?pc-groups. We study some properties of ? pc-groups and describe the structure of ?pc-groups when ? is the class of all soluble π-closed groups, where π is a given nonempty set of prime numbers. 相似文献
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Let G be a finite group and σ?=?{σi|i∈I} some partition of the set of all primes. A subgroup A of G is said to be generalized σ-subnormal in G if A?=??L,T?, where L is a modular subgroup and T is a σ-subnormal subgroup of G. In this paper, we prove that if every Schmidt subgroup of G is generalized σ-subnormal in G, then the commutator subgroup G′ of G is σ-nilpotent. 相似文献
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SKIBA Alexander N. 《中国科学 数学(英文版)》2011,(9)
In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = ... 相似文献
10.
Long Miao 《Mathematical Notes》2009,86(5-6):655-664
A subgroup H of a group G is said to be ?-supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H. In this paper, we obtain the following statement: Let ? be a saturated formation containing all supersolvable groups and H be a normal subgroup of G such that G/H ε ?. Suppose that every maximal subgroup of a noncyclic Sylow subgroup of F*(H), having no supersolvable supplement in G, is ?-supplemented in G. Then G ε ?. 相似文献
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Let G be a finite group and σ = {σ i |i∈I} be a partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every non-identity member of H is a Hall σ i -subgroup of G and H contains exactly one Hall σ i -subgroup of G for every σ i ∈ σ(G). A subgroup H is said to be σ-permutable if G possesses a complete Hall σ-set H such that HA x = A x H for all A ∈ H and all x ∈ G. Let H be a subgroup of G. Then we say that: (1) H is σ-embedded in G if there exists a σ-permutable subgroup T of G such that HT = H σG and H ∩ T ≤ H σG , where H σG is the subgroup of H generated by all those subgroups of H which are σ-permutable in G, and H σG is the σ-permutable closure of H, that is, the intersection of all σ-permutable subgroups of G containing H. (2) H is σ-n-embedded in G if there exists a normal subgroup T of G such that HT = H G and H ∩ T ≤ H σG . In this paper, we study the properties of the new embedding subgroups and use them to determine the structure of finite groups. 相似文献
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In this paper, we study the problem concerning the influence of the structure of the solvable subgroups of a groups on the structure of the group. We improved upon a series of results of Mazurov, Sitnikov, Syskin, Ogarkov, Li Shirong and Zhao Yaoqing. 相似文献
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Klaus DENECKE 《中国科学A辑(英文版)》2007,50(5):715-726
Let G be a finite group and S be a finite simple group. In this paper, we prove that if G and S have the same sets of all orders of solvable subgroups, then G is isomorphic to S, or G and S are isomorphic to Bn(q), Cn(q), where n≥3 and q is odd. This gives a positive answer to the problem put forward by Abe and Iiyori. 相似文献
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V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):22-31
Finite simple nonabelian groups G that are not π-closed for some set of primes π but have π-closed maximal subgroups (property (*) for (G, π)) are studied. We give a list L of finite simple groups that contains any group G with the above property (for some π). It is proved that 2 ? π for any pair (G, π) with property (*) (Theorem 1). In addition, we specify for any sporadic simple group G from L all sets of primes π such that the pair (G, π) has property (*) (Theorem 2). The proof uses the author’s results on the control of prime spectra of finite simple groups. 相似文献
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A. V. Tushev 《Ukrainian Mathematical Journal》1990,42(5):599-602
We study just infinite JG-modules, where J is either the -group algebra or the Ft-group algebra of the infinite cyclic group t over a finite field F and G is a solvable group of finite rank. With the help of the obtained results it is proved that the finitely approximated torsionfree solvable groups with the condition Min-- N are minimax.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 677–681, May, 1990. 相似文献
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Let q??3 be a prime and let H(?? q ) be the Hecke group associated to q. Let m be a positive integer and H m (?? q ) be the mth power subgroup of H(?? q ). In this work, we study the commutator subgroups of the power subgroups H m (?? q ) of H(?? q ). Then, we give the derived series for all triangle groups of the form (0;2,q,n) for n a positive integer, since there is a nice connection between the signatures of the subgroups we studied and the signatures of these derived series. 相似文献
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