共查询到20条相似文献,搜索用时 15 毫秒
1.
A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite derived
subgroup. This result is generalized here, by proving that every locally graded group with finitely many derived subgroups
of non-normal subgroups has finite derived subgroup. Moreover, locally graded groups having only finitely many derived subgroups
of infinite non-normal subgroups are completely described.
Received: 25 April 2005 相似文献
2.
《Expositiones Mathematicae》2021,39(3):354-368
Since solitary subgroups of (infinite) Abelian groups are precisely the strictly invariant subgroups which are co-Hopfian (as groups), and strictly invariant subgroups turn out to be strongly invariant for large classes of Abelian groups we determine the solitary subgroups for these classes of groups. 相似文献
3.
We study the groups for which the derived subgroups of all proper subgroups are Chernikov subgroups under condition that they
possess a normal system whose factors are locally graduated. 相似文献
4.
We study finite groups whose maximal subgroups of Sylow subgroups are permutable with maximal subgroups.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1299–1309, October, 2006. 相似文献
5.
W. Mack Hill 《Israel Journal of Mathematics》1977,26(1):68-74
In the context of the problem of which nonabelianp-groups can occur as normal subgroups contained in Frattini subgroups, the family of supernilpotent groups (all maximal subgroups characteristic) is investigated. Results of this investigation are applied to the Frattini-embedding problem, incorporating recent work of A. R. Makan. The groups of order 2n (n ≦ 6) have been examined with respect to supernilpotence and their occurrence as normal subgroups contained in Frattini subgroups. Results of this examination are presented. 相似文献
6.
Rose Morris-Wright 《Journal of Pure and Applied Algebra》2021,225(1):106468
Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic. 相似文献
7.
We prove that the affine-triangular subgroups are Borel subgroups of Cremona groups.
相似文献8.
Avino’am Mann 《Israel Journal of Mathematics》1968,6(1):13-25
A group is said to have dense normal subgroups, if each non-empty open interval in its lattice of subgroups contains a normal
subgroup. The structure of this and related classes of groups is investigated. Typical results are: an infinite group with
dense ascendant subgroups is locally nilpotent: a nontorsion group with dense normal subgroups is abelian, etc. 相似文献
9.
Panagiotis Soules 《Archiv der Mathematik》2003,80(5):449-457
For soluble groups, the Fitting length is bounded by a function of the maximum order
of the Fitting subgroups of 2-generator subgroups. 相似文献
10.
LetX be a torsion-free abelian group. We study the class of all completely decomposable subgroups ofX which are maximal with respect to inclusion. These groups are called tight subgroups ofX and we state sufficient conditions on a subgroup to be tight. In particular we consider tight subgroups of bounded completely
decomposable groups. For those we show that every regulating subgroup is tight and we characterize the tight subgroups of
finite index in almost completely decomposable groups.
The second author was supported by a MINERVA fellowship. 相似文献
11.
A. R. Chekhlov 《Journal of Mathematical Sciences》2010,164(1):143-147
The properties of projective invariant subgroups are studied. The structure of these subgroups in nonreduced groups is described.
The conditions under which projective invariant subgroups are fully invariant are considered. 相似文献
12.
E. P. Vdovin 《Siberian Advances in Mathematics》2009,19(1):24-74
It is proven that the Carter subgroups of a finite group are conjugate. A complete classification of the Carter subgroups in finite almost simple groups is also obtained. 相似文献
13.
AbstractIn this paper, we introduce the concept of sse-embedded subgroups of finite groups and present some new characterizations of solubility of finite groups using the sse-embedding property of subgroups. Furthermore, we discuss the sse-embedded subgroups in finite nonabelian simple groups. Some previously known results are generalized and unified. 相似文献
14.
Describing intermediately fully invariant subgroups of divisible and torsion groups, we show that the intermediately fully invariant subgroups are direct summands in a completely decomposable group whose every homogeneous component is decomposable. For torsion groups, we find out when all their fully invariant subgroups are intermediately fully invariant; and for torsion-free groups, this question comes down to the reduced case. Also, in a torsion group that is the sum of cyclic subgroups, its subgroup is shown to be intermediately inert if and only if it is commensurable with some intermediately fully invariant subgroup. 相似文献
15.
We investigate separability questions for the mapping class group of a surface. While this group is not subgroup separable in general, we prove a large family of interesting subgroups are separable. This includes many classically studied subgroups such as solvable subgroups, Heegaard and Handlebody groups, geometric subgroups, and all the terms in the Johnson filtration. 相似文献
16.
Arithmetic subgroups of simple isotropic algebraic groups are described as subgroups full of root elements. 相似文献
17.
The structure of groups with finitely many non-normal subgroups is well known. In this paper, groups are investigated with
finitely many conjugacy classes of non-normal subgroups with a given property. In particular, it is proved that a locally
soluble group with finitely many non-trivial conjugacy classes of non-abelian subgroups has finite commutator subgroup. This
result generalizes a theorem by Romalis and Sesekin on groups in which every non-abelian subgroup is normal.
相似文献
18.
On complemented subgroups of finite groups 总被引:3,自引:0,他引:3
In this paper, it is proved that the class of all finite supersoluble groups with elementary abelian Sylow subgroups is just the class of all finite groups for which every minimal subgroup is complemented. The structure of a finite group under the assumption that all maximal subgroups (respectively 2-maximal) of any Sylow subgroup are complemented is also analyzed. 相似文献
19.
Maria De Falco Francesco de Giovanni 《Bulletin of the Brazilian Mathematical Society》2000,31(1):73-80
A group is said to be aT-group if all its subnormal subgroups are normal. The structure of groups satisfying the minimal condition on subgroups that do not have the propertyT is investigated. Moreover, locally soluble groups with finitely many conjugacy classes of subgroups which are notT-groups are characterized. 相似文献
20.
Mariagrazia Bianchi Anna Gillio Berta Mauri Peter Hauck 《Annali di Matematica Pura ed Applicata》1991,159(1):371-404
Summary All maximal supersoluble subgroups of symmetric groups are classified. 相似文献