Related papers: On groups that have normal forms computable in log…

In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…

We give new and improved results on the freeness of subgroups of free profinite groups: A subgroup containing the normal closure of a finite word in the elements of a basis is free; Every infinite index subgroup of a finitely generated…

Let $\mathcal G$ denote the space of finitely generated marked groups. We give equivalent characterizations of closed subspaces $\mathcal S\subseteq \mathcal G$ satisfying the following zero-one law: for any sentence $\sigma$ in the…

The aim of this paper is to compare and contrast the class of residually finite groups with the class of equationally Noetherian groups - groups over which every system of coefficient-free equations is equivalent to a finite subsystem. It…

We explore the graded and filtered formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie…

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

We study the structure of discrete subgroups of the group $G[[r]]$ of complex formal power series under the operation of composition of series. In particular, we prove that every finitely generated fully residually free group is embeddable…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…

We introduce a formalism of infinite, linearly ordered products in general groups. Using this, we define infinite compositions in certain groups of formal power series such as transseries. We show that such groups can sometimes be…

Every finite group $G$ has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length $\lambda (G)$ as the minimum number of nonsoluble factors in a series of…

We show that every finitely generated extension by $\mathbb{Z}$ of a locally normally finite group has Shalom's property $H_{\mathrm{FD}}$. This is no longer true without the normality assumption. This permits to answer some questions of…

A finitely generated group G is termed parafree if it is residually nilpotent and it has the same isomorphism types of nilpotent quotients as some free group. The two main results of this MSc. Thesis characterise the parafreeness of two…

In this work we first give for PN spaces results parallel to those obtained by Egbert for the product of PM spaces, and generalize results by Alsina and Schweizer in order to study non-trivial products and the product of $m$-- transforms of…

We give a description of elementary subgroups (in the sense of first-order logic) of finitely generated virtually free groups. In particular, we recover the fact that elementary subgroups of finitely generated free groups are free factors.…

In the paper the class of all solvable extensions of a filiform Leibniz algebra in the infinite-dimensional case is classified. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of residually solvable Leibniz algebra.…

We show that a free action $G \curvearrowright X$ is almost finite if its restriction to some infinite normal subgroup of $G$ is almost finite. Consider the class of groups which contains all infinite groups of locally subexponential growth…

We examine the question of which finitely generated groups act properly on a finite product of locally finite simplicial trees and present evidence in favour of hyperbolic surface groups having such an action. We also give a completely…

We prove that a finitely generated solvable group which is not virtually nilpotent has exponential conjugacy growth.

In a number of recent works, it has been established that many virtually free groups, almost all fundamental groups of surfaces and all groups which are nontrivial free products of groups satisfying a non-trivial law are algebraically…