共查询到20条相似文献,搜索用时 15 毫秒
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We establish the solvability of each finite group whose every proper nonmaximal subgroup lies in some subgroup of prime index. 相似文献
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For each natural number n, let a0(n) = n, and if a0(n),…,ai(n) have already been defined, let ai+1(n) > ai(n) be minimal with (ai+1(n), a0(n) … ai(n)) = 1. Let g(n) be the largest ai(n) not a prime or the square of a prime. We show that g(n) ~ n and that for some c > 0. The true order of magnitude of g(n) ? n seems to be connected with the fine distribution of prime numbers. We also show that “most” ai(n) that are not primes or squares of primes are products of two distinct primes. A result of independent interest comes of one of our proofs: For every sufficiently large n there is a prime with [] composite. 相似文献
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V. A. Antonov 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):19-24
We investigate the structure of a finite nonsolvable group G in which the index |N G (A): AC G (A)| is either one or a prime for any nonabelian subgroup A. 相似文献
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Ruslan Iu. Ievstafiev 《Archiv der Mathematik》2008,91(1):12-19
The set of all elements of an associative ring R, not necessarily with a unit element, forms a monoid under the circle operation a ° b = a + b + ab. The group of all invertible elements of this monoid is called the adjoint group of R and is denoted by R
°. It is proved that an artinian ring R with supersolvable adjoint group R
° must be Lie supersolvable. An example of a Lie supersolvable ring with non-supersolvable adjoint group is also constructed.
Received: 7 December 2007 相似文献
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In the paper, the finite groups G are studied for which every invariant subgroup A has the property that |G: AC G (A)| divides a fixed prime p. 相似文献
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V. S. Monakhov 《Mathematical Notes》2013,93(3-4):460-464
The solvability of a finite group G = AB is established under the assumption that the subgroups A and B are solvable and the Carter subgroups of A commute with the Carter subgroups of B. 相似文献
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New criteria of existence and conjugacy of Hall subgroups of finite groups are given. 相似文献
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Jianhong Huang 《代数通讯》2019,47(3):1299-1310
In this paper, we give some new conditions under which a normal subgroup E of a finite group G is hypercyclically embedded in G, that is, every chief factor of G below E is cyclic. 相似文献
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Graham Ellis 《Archiv der Mathematik》1996,66(6):467-469
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Xianmeng Meng 《Journal of Number Theory》2005,114(1):37-65
Let N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solutions, where ni has a fixed number of prime factors, and an asymptotic formula holds for the number of representations. 相似文献
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Gábor Tardos 《Inventiones Mathematicae》1992,108(1):29-36
Summary The Hanna Neumann Conjecture says that the intersection of subgroups of rankn+1 andm+1 of a free group has rank at mostnm+1. This paper proves the conjecture for the casem=1. (See Theorem 1.) Our methods imply that the strengthened Hanna Neumann Conjecture is also true in this case (Theorem 2).Oblatum 31-V-1991 & 8-X-1991 相似文献
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AbstractThere has been some interest in understanding the relationship between the number of cyclic subgroups of a group and its order. This relationship is controlled in many cases by the size of the set of non-squares of the group. We improve upon previously established bounds and classify groups that obtain our new bound. 相似文献
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Shi Rong Li 《数学学报(英文版)》2008,24(4):647-654
Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown: (1) G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; (2) G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F(H), the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G. 相似文献