Related papers: Finite Localities I
We give two examples of a finitely generated subgroup of a free group and a subset, closed in the profinite topology of a free group, such that their product is not closed in the profinite topology of a free group.
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.
In this article, we prove that a semidirect product of a locally finite group with a surjunctive group is also surjunctive. We also prove that a surjunctive-by-locally finite group is again surjunctive.
A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generalization of Hamiltonian groups. In this paper, the properties of finite metahamiltonian $p$-groups are investigated.
We develop a theory of direct and central products of partial groups and localities.
We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible…
We prove that the free product of two finitely presented locally tame groups is locally tame and describe many examples of tame subgroups of finitely presented groups. We also include some open problems related to tame subgroups.
In this paper we shall investigate the concepts of cofiniteness of local cohomology modules and Abelian categories of cofinite modules over arbitrary Noetherian rings. Then we shall improve some of the results given in the literature.
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability. We construct a finitely generated, residually finite, amenable group $A$ and an uncountable…
This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…
We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the…
We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.
In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.
In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgroups or, more strongly, normal subgroups with Kazhdan's…
The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a…
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…
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
We give the canonical normal form for the elements of the finite or infinite alternating groups using local stationary presentation of these groups.