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251.
252.
Let N be a normal subgroup of a group G. Suppose that the positive integers m 〉 n are two longest non-central G-conjugacy class sizes of N with (m, n) = 1. The purpose of this paper is to determine the structure of N and give the N-conjugacy class sizes of the elements in N under that assumption that m is square free. 相似文献
253.
ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS 总被引:1,自引:0,他引:1
A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F(G), where Z∞F(G) is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups. 相似文献
254.
S. F. Kamornikov 《Siberian Mathematical Journal》2008,49(6):1044-1050
We study the partially prefrattini groups of a finite soluble group. We prove that the set of all partially prefrattini subgroups associated with the Gaschütz system of complements to crowns is a Boolean lattice. 相似文献
255.
In this paper, the famous Hall theorem and the famous Schur-Zassenhaus theorem are generalized. 相似文献
256.
A subgroup of index p k of a finite p-group G is called a k-maximal subgroup of G. Denote by d(G) the number of elements in a minimal generator-system of G and by δ k (G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G. In this paper, the authors classify the finite p-groups with δd(G)(G) ≤ p2 and δd(G)?1(G) = 0, respectively. 相似文献
257.
Let A be a subgroup of a group G and X a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we try to use the X-semipermutability of some subgroups to characterize the structure of finite groups. 相似文献
258.
Lydia Außenhofer 《Journal of Mathematical Analysis and Applications》2010,370(2):431-570
The aim of this paper is to go deeper into the study of local minimality and its connection to some naturally related properties. A Hausdorff topological group (G,τ) is called locally minimal if there exists a neighborhood U of 0 in τ such that U fails to be a neighborhood of zero in any Hausdorff group topology on G which is strictly coarser than τ. Examples of locally minimal groups are all subgroups of Banach-Lie groups, all locally compact groups and all minimal groups. Motivated by the fact that locally compact NSS groups are Lie groups, we study the connection between local minimality and the NSS property, establishing that under certain conditions, locally minimal NSS groups are metrizable. A symmetric subset of an abelian group containing zero is said to be a GTG set if it generates a group topology in an analogous way as convex and symmetric subsets are unit balls for pseudonorms on a vector space. We consider topological groups which have a neighborhood basis at zero consisting of GTG sets. Examples of these locally GTG groups are: locally pseudoconvex spaces, groups uniformly free from small subgroups (UFSS groups) and locally compact abelian groups. The precise relation between these classes of groups is obtained: a topological abelian group is UFSS if and only if it is locally minimal, locally GTG and NSS. We develop a universal construction of GTG sets in arbitrary non-discrete metric abelian groups, that generates a strictly finer non-discrete UFSS topology and we characterize the metrizable abelian groups admitting a strictly finer non-discrete UFSS group topology. Unlike the minimal topologies, the locally minimal ones are always available on “large” groups. To support this line, we prove that a bounded abelian group G admits a non-discrete locally minimal and locally GTG group topology iff |G|?c. 相似文献
259.
Gábor Elek 《Journal of Functional Analysis》2018,274(6):1657-1689
We study uniformly recurrent subgroups (URS) introduced by Glasner and Weiss [18]. Answering their query we show that any URS Z of a finitely generated group is the stability system of a minimal Z-proper action. We also show that for any sofic URS Z there is a Z-proper action admitting an invariant measure. We prove that for a URS Z all Z-proper actions admits an invariant measure if and only if Z is coamenable. In the second part of the paper we study the separable -algebras associated to URS's. We prove that if a URS is generic then its -algebra is simple. We give various examples of generic URS's with exact and nuclear -algebras and an example of a URS Z for which the associated simple -algebra is not exact and not even locally reflexive, in particular, it admits both a uniformly amenable trace and a nonuniformly amenable trace. 相似文献
260.
Let K be a field of characteristic p>0 and let KG be the group algebra of an arbitrary group G over K. It is known that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least p+1. The group algebras KG for which these indices are p+1 or 2p or 3p?1 or 4p?2 have already been determined. In this paper, we classify the group algebras KG for which the upper Lie nilpotency index is 5p?3, 6p?4 or 7p?5. 相似文献