Related papers: Groups with quadratic-non-quadratic Dehn functions

The generalized Fitting height of a finite group $G$ is the least number $h=h^*(G)$ such that $F^*_h(G)=G$, where the $F^*_i(G)$ is the generalized Fitting series: $F^*_1(G)=F^*(G)$ and $F^*_{i+1}(G)$ is the inverse image of…

Let $G$ be a finitely generated group acting faithfully and properly discontinuously by homeomorphisms on a planar surface $X \subseteq \mathbb{S}^2$. We prove that $G$ admits such an action that is in addition co-compact, provided we can…

The functions $F_{G}(n)$ measures the asymptotic behavior of residual finiteness for a finitely generated group $G$. In previous work \cite{Pengitore_1}, the author claimed a characterization for $F_{N}(n)$ when $N$ is a finitely generated…

For a finite group $G$, we consider the zeta function $\zeta_G(s) = \sum_{H} \abs{H}^{-s}$, where $H$ runs over the subgroups of $G$. First we give simple examples of abelian $p$-group $G$ and non-abelian $p$-group $G'$ of order $p^m, \; m…

Let $A$ be a non-metacyclic finite group. Suppose that $A$ acts coprimely on a finite group $G$ in such a manner that $C_G(a)$ is nilpotent for any $a\in A^{\#}$. In the present paper we investigate some conditions on $A$ which imply that…

Let G be a finite group and \rho: G--> End(E) be a group representation of G on a coherent sheaf over an integral scheme. The purpose of this paper shall give a decomposition theorem of such representations in non-splitting components and…

Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In…

This is a survey of the recent work in algorithmic and asymptotic properties of groups. I discuss Dehn functions of groups, complexity of the word problem, Higman embeddings, and constructions of finitely presented groups with extreme…

We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.

We analyze Fourier hyperfunction and hyperfunction semigroups with non-densely defined generators and their connections with local convoluted $C$-semigroups. Structural theorems and spectral characterizations give necessary and sufficient…

A criterion for quadratic or higher growth of group automorphisms is established which are represented by graph-of-groups automorphisms with certain well specified properties. As a consequence, it is derived (using results of a previous…

This is the first paper in a series of three where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Our main goal is to show that group actions on Z^n-trees give one a powerful tool to…

Let N be a normal subgroup of a finite group G. We prove that under certain (unavoidable) conditions the subgroup [N,G] is a product of commutators [N,y] (with prescribed values of y from a given set Y) of length bounded by a function of…

We study finitely generated models of countable theories, having at most countably many nonisomorphic finitely generated models. We intro- duce a notion of rank of finitely generated models and we prove, when T has at most countably many…

We describe an algorithm for deciding whether or not a given finitely generated torsion-free nilpotent group is decomposable as the direct product of nontrivial subgroups.

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by…

It is proven that if $G$ is a finite group, then $G^\omega$ has $2^{\mathfrak c}$ dense nonmeasurable subgroups. Also, other examples of compact groups with dense nonmeasurable subgroups are presented.

Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In…

This paper reproduces the text of a part of the Author's DPhil thesis. It gives a proof of the classification of non-trivial, finite homogeneous geometries of sufficiently high dimension which does not depend on the classification of the…

It is shown that for any action of a finitely presented group $G$ on an $\R$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there…