Related papers: Locally finite groups of finite centraliser dimens…
We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.
The supremum of lengths of strict chains of nested centralizers is called the $c$-dimension (centralizer dimension) of $G$. We prove two structure theorems for locally finite groups of finite $c$-dimension. We also prove that the…
The c-dimension of a group G is the maximal length of a chain of nested centralizers in G. We prove that a locally finite group of finite c-dimension k has less than 5k nonabelian composition factors.
Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.
In a previous paper 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…
We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.
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 determine the finite groups whose real irreducible representations have different degrees.
We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
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…
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
We develop structure theory of finite Lie conformal superalgebras.
We study centralisers of finite order automorphisms of generalisations of Thompson's group F and conjugacy classes of finite subgroups in finite extensions of these groups. In particular, we show that centralisers of finite automorphisms in…