Related papers: On finite groups with dismantlable subgroup lattic…
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…
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…
The subgroup generated by all solvable normal subgroups in a pseudo-finite group with the descending chain condition on centralizers up to finite index is solvable. Additionally, there is no finitely generated pseudo-finite group whose…
We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and…
We construct integrable modifications of 2d lattice gauge theories with finite gauge groups.
We describe here the lower garland of some lattices of intermediate subgroups in linear groups. The results are applied to the case of subgroup lattices in general and special linear groups over a class of rings, containing the group of…
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…
This article contains a basic introduction to the local study of finite groups, including a brief perspective on the theory of fusion systems and $p$-local finite groups. -- Este art\'iculo contiene una introducci\'on b\'asica al estudio…
We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.
This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In case the generating group is cyclic, they are also known…
For a finite group G, we denote by v(G) the number of conjugacy classes of subgroups of G not in CD(G). In this paper, we determine the finite groups G such that v(G)=1,2,3.
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
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 prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.
A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups…
In this short note, we describe finite groups all of whose non-trivial cyclic subgroups have the same Chermak-Delgado measure.
In this paper, we give the definition of {\em weakly locally finite} division rings and we show that the class of these rings strictly contains the class of locally finite division rings. Further, we study multiplicative subgroups in these…
In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible…
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank…
In this note, we classify all finite groups having exactly 6, 7 or 8 cyclic subgroups. This gives a partial answer to the open problem posed by Tarnauceanu (Amer. Math. Monthly, 122 (2015), 275-276). As a consequence of our results, we also…