Related papers: An incoherent simple group
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.
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite…
A recent conjecture of the author and Teng Fang states that there are only finitely many finite simple groups with no cubic graphical regular representation. In this paper, we make a crucial progress towards this conjecture by giving an…
Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal…
In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.
A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups are either: finite, or of finite index,…
We consider the group property of being icc. We give several examples of icc groups and study its stability under usual algebraic constructions.
We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely presented counterexample to von Neumann's problem. Our group is an extension of a group of finite exponent n >> 1 by a cyclic…
The spectra of a finite group is the set of its element orders. We obtain an arithmetic description of finite symplectic and orthogonal groups. In particular, a description of spectra of all finite simple simplectic and orthogonal groups is…
In this note a very simple example is given which shows that if the sum of two semigroup generators is itself a generator, the generated semigroup in general can not be rapresented by the Lie-Trotter product formula.
In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.
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…
We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.
In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.
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…
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) \leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing…
A subgroup of a finite group is wide if each prime divisor of the group order divides the subgroup order. We obtain the description of finite soluble groups with no wide subgroups. We also prove that a finite soluble group with nilpotent…
This paper surveys basic properties of finite presentation in groups, Lie algebras and rings. It includes some new results and also new, more elementary proofs, of some results that are already in the literature. In particular, we discuss…
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained in a generating set of minimal size if and only if all proper quotients of G require fewer generators than G. It is natural to ask which…
The goal of this article is to exhibit two new families of finitely generated simple groups of homeomorphisms of $\mathbf{R}$. These families are strikingly different from existing families owing to the nature of their actions on…