Related papers: Non-linear residually finite groups

For every natural number $n$, there exist finitely presented groups with residual finiteness depths $\omega\cdot n$ and $\omega\cdot n + 1$. The ordinals that arise as the residual finiteness depth of a finitely generated group…

We establish conditions under which the fundamental group of a graph of finite $p$-groups is necessarily residually $p$-finite. The technique of proof is independent of previously established results of this type, and the result is also…

We construct the first examples of residually finite amenable groups that are not Hilbert-Schmidt (HS) stable. We construct finitely generated, class 3 nilpotent by cyclic examples and solvable linear finitely presented examples. This also…

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We show that for any pair of non-trivial finite groups, their coproduct in the category of finite groups is not representable.

The first-order theory of the automorphism group of an infinite resplendent model in a finite language is undecidable.

An irreducible character $\chi$ of an association scheme is called nonlinear if the multiplicity of $\chi$ is greater than $1$. The main result of this paper gives a characterization of commutative association schemes with at most two…

Here we show that a finite nilpotent group is 2-closed if and only if it is either cyclic or a direct product of a generalized quaternion group with a cyclic group of odd order.

In this paper, we classify the finite simple groups with an abelian Sylow subgroup.

In this note, we study the finite groups with the number of cylic subgroups no greater than 6.

We construct a 2-generated 2-related group without non-trivial finite factors. That answers a question of J. Button.

A cover of a finite non-cyclic group $G$ is a family $\mathcal{H}$ of proper subgroups of $G$ whose union equals $G$. A cover of $G$ is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover.…

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit…

Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked…

We introduce a new real valued invariant for finitely presented groups called residual deficiency. Its main property is the following. Let G be a finitely presented group. If the residual deficiency of G is greater than one, then G has a…

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…

We construct first examples of infinite groups having property (T) whose Kazhdan constants admit a lower bound independent of the choice of a finite generating set.

In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…

An $integral$ of a group $G$ is a group $H$ whose derived group (commutator subgroup) is isomorphic to $G$. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those…

Let p be a prime. Every finite group G has a normal series each of whose quotients either is p-soluble or is a direct product of nonabelian simple groups of orders divisible by p. The non-p-soluble length of G is defined as the minimal…