Partially Commutative Metabelian Pro-P-Groups

Siberian Mathematical Journal - We prove two theorems about a partially commutative metabelian pro-p-group. The first theorem concerns the structure of annihilators for the commutators of...     

Centraliser Dimension of Partially Commutative Groups

In a previous paper (Centraliser Dimension and Universal Classes of Groups), we investigated the centraliser dimension of groups. In the current paper we study properties of centraliser dimension for the class of free partially commutative groups and, as a corollary, we obtain an efficient algorithm for computation of centraliser dimension in these groups.Ilya V. Kazachkov, Vladimir N. Remeslennikov: Supported by RFFI grant N05-01-00057-a     

n—反Abelian子群

从n-反换位子群的定义出发,得到了它的几条重要性质.作为应用,给出了一个群为n-反A belian群的一个充要条件及p-反A belian群的一个判别法.     

Convex Subgroups of Partially Right-Ordered Groups

We study into the question of whether a partial order can be induced from a partially right-ordered group onto a space of right cosets of w.r.t. some subgroup of . Examples are constructed showing that the condition of being convex for in is insufficient for this. A necessary and sufficient condition (in terms of a subgroup and a positive cone of ) is specified under which an order of can be induced onto . Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups for which is partially ordered for every convex subgroup , and properties of the class of groups such that is partially ordered for every partial right order on and every subgroup that is convex under .     

A Basis for the Commutator Subgroup of a Partially Commutative Metabelian Pro-p-Group

Algebra and Logic - A basis for the commutator subgroup of a partially commutative metabelian pro-p-group is described.     

On Nilpotent and Metabelian Products of Groups

This work is devoted to the study of properties of verbal products and interlacings of groups. More precisely we study approximation properties (for example, the finite approximability, approximability by finite p-groups, and so on) of nilpotent and metabelian products and interlacings. We apply verbal interlacings to the problem of finite approximability with respect to the conjugacy for some nilpotent interlacings and to the study of stable automorphisms of groups of the form $ {F \left/ {V} \right.}\left( \mathcal{N} \right) $ .     

Finite Groups with Weakly Subnormal and Partially Subnormal Subgroups

Siberian Mathematical Journal - We study the influence of weakly subnormal and partially subnormal subgroups on the structure of a group  $ G $ . In particular, we prove that a...     

Wavelet Transforms for Semidirect Product Groups with Not Necessarily Commutative Normal Subgroups

Let G be the semidirect product group of a separable locally compact unimodular group N of type I with a closed subgroup H of Aut(N). The group N is not necessarily commutative. We consider irreducible subrepresentations of the unitary representation of G realized naturally on L²(N), and investigate the wavelet transforms associated to them. Furthermore, the irreducible subspaces are characterized by certain singular integrals on N analogous to the Cauchy-Szegö integral.     

Metabelian Products of Groups

We prove a number of facts on metabelian products of metabelian groups, useful in algebraic geometry over groups. Namely, for a metabelian product of arbitrary metabelian groups, we look at the structure of a derived subgroup, and the Fitting radical; find criteria determining when a metabelian product of u-groups is again a u-group; and specify conditions under which a metabelian product of metabelian groups is a strong semidomain.     

On Partially Commutative Groups and the Relevant Algebras with Commutation

Siberian Mathematical Journal - We consider the algebra $ G_{\circ} $ with commutation on the set of the elements of a partially commutative metabelian group  $ G $ . Under study is the...     

Embedding Properties of Metabelian Lie Algebras and Metabelian Discrete Groups

We show that for every natural number m a finitely generatedmetabelian group G embeds in a quotient of a metabelian groupof type FP_m. Furthermore, if m 4, the group G can be embeddedin a metabelian group of type FP_m. For L a finitely generatedmetabelian Lie algebra over a field K and a natural number mwe show that, provided the characteristic p of K is 0 or p >m, then L can be embedded in a metabelian Lie algebra of typeFP_m. This result is the best possible as for 0 < p m everymetabelian Lie algebra over K of type FP_m is finite dimensionalas a vector space.     

On Subgroups and Quotient Groups of L-fuzzy Topological Groups

In paper [1], it gave the concept and basic properties of L-fuzzy topological groups. This paper will enter the concept of quotient groups of L-fuzzy topological groups and will prove some properties of subgroups and quotient groups. The persent work is the continuation of [1] and hence all the conventions in [1] still hold good in the present paper.     

On Fisher Subgroups of Finite Groups

Ukrainian Mathematical Journal - Let ? be a Fitting set of a group G, let π be a nonempty set of primes, and let L ≤ G. In this case, ? is called a Fischer π-set of G if...     

On the Decomposition of Partially Commutative Groups of Varieties and Their Defining Graphs

Siberian Mathematical Journal - Considering the partially commutative groups of&nbsp;varieties which contain the variety of all nilpotent groups of&nbsp;class&nbsp;2 as well as the...     

On c-Normal Subgroups of Finite Groups

A subgroup H is said to be c-normal in a group G if there exists a normal subgroup K of G such that G = HK and H K is contained in H_G, where H_G is the maximal normal subgroup of G. We determine the structures of some groups in which some primary subgroups is c-normal.AMS Mathematics Subject Classification (2000) 20D10 20D20