有限群的Fuzzy拟正规子群和Fuzzy次正规子群

讨论有限群的Fuzzy拟正规子群和Fuzzy次正规子群的一些性质。     

有限群的Fuzzy次正规子群与Fuzzy极大子群

本文研究了有限群的Ｆ次正规子群，得出了一个Ｆ子群是Ｆ次正规子群的充要条件，讨论了Ｆ次正规子群的一些重要性质。另外，本文还引入了有限群的Ｆ极大子群的概念，给出了Ｆ子群是Ｆ极大群的充要条件。最后，给出了三个定理，讨论了有限群Ｇ可解、超可解、幂零与Ｇ的Ｆ次正规子群、Ｆ极大子群之间的联系。     

Fine Control over the Projective Characters of the Centre of a Group

In this article we will study the restriction of the irreducible projective characters of a finite group to a central subgroup. We will also consider under what conditions on the restriction of such irreducible projective characters to an abelian normal subgroup that we can deduce that the subgroup is central. Finally, we will investigate the relationship between the inertia subgroup and the absolute centralizer of a central subgroup relative to a fixed 2-cocycle of the group.     

The Intersection of a Maximal Intransitive Subgroup with a Maximal Imprimitive Subgroup

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非极大交换子群皆正规的有限群

设H是有限群G的一个交换子群.如果H在G中的中心化子正是它本身,则称H为G的极大交换子群.本文主要研究每一非极大交换子群都正规的有限群的结构,对这类有限群给出其完全分类.     

Pseudocomplementation in (Normal) Subgroup Lattices

The goal of this article is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a Stone normal subgroup lattice. Finally, we obtain a complete classification of finite groups for which every subgroup is monolithic.     

On SS-quasinormal subgroups and the structure of finite groups

A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpo...     

灰色数学的新分支——灰群

给出灰子半群、强灰子半群、灰子幺半群、强灰子幺半群、灰子群和强灰子群的定义和有关定理，在此基础上，讨论灰子群一模糊子群、一般子群的关系。并且研究了灰正规子群。     

Abelian subgroup separability of certain generalized free products of free or finitely generated nilpotent groups

In this paper we prove that certain generalized free products of abelian subgroup separable groups, amalgamating an infinite cyclic subgroup, are abelian subgroup separable. Applying this, we derive that tree products of free groups or finitely generated nilpotent groups, amalgamating infinite cyclic subgroups, are abelian subgroup separable.     

p-Fitting子群的CAP-嵌入子群

群G的子群H称为G的CAP-嵌入子群,如果对于|H|的每个素因子p,存在G的某个CAP-子群K,使得H的某个Sylow p-子群也是K的一个Sylowp-子群.本文通过假定G的p-Fitting子群F_p(G)的某个Sylow p-子群的每个极大子群是G的CAP-嵌入子群,得到一些新的结果.     

Large characteristic subgroups with modular subgroup lattice

It is known that if a group contains an abelian subgroup of finite index, then it also has an abelian characteristic subgroup of finite index. The aim of this paper is to prove that corresponding results hold when abelian subgroups are replaced either by subgroups having a modular subgroup lattice or by quasihamiltonian subgroups.     

R-模糊正规子群

给出了R-模糊正规子群与基于蕴涵的模糊正规子群的定义,得到了R-模糊正规子群的交、并、同态像以及同态原像的相关性质;另外还讨论了它与不同的模糊正规子群的区别与联系,并且给出了具体的蕴涵算子厦它的等价形式.     

Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup

In this paper, we obtain a complete classification of finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup.     

An action of subgroups of mapping class groups on polynomial algebras

We study a certain subgroup of the mapping class group of a surface with boundary by obtaining an action of this subgroup on a polynomial algebra. This action comes from a lift of the action of the subgroup on a trace algebra, Magnus having done a similar thing for the braid groups. We then investigate the invariant theory for this action and various representations that this action affords. In particular, we obtain finite permutation representations and infinite linear representations of these subgroups that are non-trivial on subgroups of the Torelli group.     

The Influence of Primitive Subgroups on the Structure of Finite Groups

A subgroup $H$ of a group $G$ is said to be primitive if it is a proper subgroup of the intersection of all subgroups of $G$ containing $H$ as its proper subgroup. The purpose of this note is to go further into the influence of primitive subgroups on the structure of finite groups. Some new results are obtained.     

The Generalised Pro-Fitting Subgroup of a Profinite Group

The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, so that any finite group is an abelian extension of a group of automorphisms of its generalised Fitting subgroup. We define a class of profinite groups which generalises this phenomenon, and explore some consequences for the structure of profinite groups.     

生成反模糊子群

引入生成反模糊子群的概念,给出生成反模糊子群的代数刻画式,讨论了生成反模糊子群的基本性质.     

Notes on NE-subgroups of finite groups

In this paper, we first analyze the structure of a finite nonsolvable group in which every cyclic subgroup of order 2 and 4 of every second maximal subgroup is an NE-subgroup. Next, we prove that a finite group G is solvable if every nonnilpotent subgroup of G is a PE-group.     

模糊子群的阶的注记

讨论一个群G的模糊子群μ的阶与μ所对应的子群链之间的关系和具有有限生成元的阿贝尔群的阶与其模糊子群的阶的关系，并得到了一些相关结果。     

Characterization of Finite Groups With Some S-quasinormal Subgroups

A subgroup of a finite group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. In this paper we give a characterization of a finite group G under the assumption that every subgroup of the generalized Fitting subgroup of prime order is S-quasinormal in G.