Related papers: A note on localizations of perfect groups
We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer…
We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…
We point out some minor errors in a paper by the first author, and explain why they do not affect the main results in the paper.
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group…
We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe the structure of soluble groups and finite perfect groups with…
The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…
Let $p$ be a prime, $P$ a finite p-group and $\cal F$ a Frobenius $P$-category. In "Existence, uniqueness and functoriality of the perfect locality over a Frobenius $P$-category", Algebra Colloquium, 23(2016) 541-622, we also claimed the…
In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…
This paper extends the study of group algebras of finite groups in which the socle of the center is an ideal. We provide a detailed analysis of the structure of these groups. In a particular case, we reach a complete characterization of the…
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
We introduce the notion of soficity for locally compact groups and list a number of open problems.
Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal…
Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.
We construct a finitely generated 2-dimensional group that acts properly on a locally finite CAT(0) cube complex but does not act properly on a finite dimensional CAT(0) cube complex.
A group homomorphism eta:A-> H is called a localization of A if every homomorphism phi:A-> H can be `extended uniquely' to a homomorphism Phi:H-> H in the sense that Phi eta = phi. This categorical concepts, obviously not depending on the…
Let $G$ be a group and let $K$ be a commensurated subgroup of $G$. Then there is a totally disconnected, locally compact (t.d.l.c.) group $\hat{G}_K$ that contains the profinite completion of $K$ as an open compact subgroup and also…
We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.