Related papers: Universal solvability of group equations

The Boone--Higman conjecture is that every recursively presented group with solvable word problem embeds in a finitely presented simple group. We discuss a brief history of this conjecture and work towards it. Along the way we describe some…

We formulate, and provide strong evidence for, a natural generalization of a conjecture of Robert Coleman concerning Euler systems for the multiplicative group over arbitrary number fields.

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

We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton--Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.

We prove the decidability of the elementary theory of a free group.

In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…

We give a determination of the equivalence group of Euler-Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.

We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…

We prove a conjecture of Shafarevich about universal coverings of projective manifolds provided the fundamental group is residually finite.

We first prove that the Whitehead group of a torsion-free virtually solvable linear group vanishes. Next we make a reduction of the fibered isomorphism conjecture from virtually solvable groups to a class of virtually solvable Q-linear…

The Andrews-Curtis conjecture claims that every normally generating $n$-tuple of a free group $F_n$ of rank $n \ge 2$ can be reduced to a basis by means of Nielsen transformations and arbitrary conjugations. Replacing $F_n$ by an arbitrary…

We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the…

The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or not. We show that the Equation Problem in central extensions…

Every finite non-nilpotent group can be extended by a term operation such that solving equations in the resulting algebra is NP-complete and checking identities is co-NP-complete. This result was firstly proven by Horv\'ath and Szab\'o; the…

In a first part, we give a new proof of Koenigs theorem and, in a second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their global geometries.

We discuss the explicit construction of the Schroedinger equations admitting a representation through some family of general polynomials. Almost all solvable quantum potentials are shown to be generated by this approach. Some generalization…

This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…

In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this circle of ideas, we resolve a conjecture of Bremner on…

Using the basic prolongation method and the infinitesimal criterion of invariance, we find the most general Lie point symmetries group of the Thomas equation. Looking the adjoint representation of the obtained symmetry group on its Lie…

Let $R=K[G]$ be a group ring of a group $G$ over a field $K$. It is known that if $G$ is amenable then $R$ satisfies the Ore condition: for any $a,b\in R$ there exist $u,v\in R$ such that $au=bv$, where $u\ne0$ or $v\ne0$. It is also true…