Related papers: Residually rationally solvable one-relator groups

In this paper we study the satisfiability and solutions of group equations when combinatorial, algebraic and language-theoretic constraints are imposed on the solutions. We show that the solutions to equations with length, lexicographic…

In this paper we show that the membership problems for finitely generated submonoids and for rational subsets are recursively equivalent for groups with two or more ends.

We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising…

This note investigates and clarifies some connections between the theory of one-relator groups and special one-relation inverse monoids, i.e. those inverse monoids with a presentation of the form $\operatorname{Inv}\langle A \mid w=1…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.

The subgroup generated by all solvable normal subgroups in a pseudo-finite group with the descending chain condition on centralizers up to finite index is solvable. Additionally, there is no finitely generated pseudo-finite group whose…

We are looking for the smallest integer k>1 providing the following characterization of the solvable radical R(G) of any finite group G: R(G) coincides with the collection of all g such that for any k elements a_1,a_2,...,a_k the subgroup…

Let $G$ be a semisimple affine algebraic group defined over a field $k$ of characteristic zero. We describe all the maximal connected solvable subgroups of $G$, defined over $k$, up to conjugation by rational points of $G$.

A finite group $G$ is said to be rational if every character of $G$ is rational-valued. The Gruenberg-Kegel graph of a finite group $G$ is the undirected graph whose vertices are the primes dividing the order of $G$ and the edges join…

In this paper, we show that each finite group $G$ containing at most $p^2$ Sylow $p$-subgroups for each odd prime number $p$, is a solvable group. In fact, we give a positive answer to the conjecture in \cite{Rob}.

Let G be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of G is polycyclic. Then the claim is made that any solvable subgroup of G is separable. This is proven for G=SL_n(Z).…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an…

We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…

We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.

Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex numbers.

We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where is the line separating positive and negative solutions to the Isomorphism Problem for…

We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular,…

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