相关论文: The conjugacy and isomorphism problems for combabl…

We show that for topological groups and loop contractible coefficients the cohomology groups of continuous group cochains and of group cochains that are continuous on some identity neighbourhood are isomorphic. Moreover, we show a similar…

Let $n\in \mathbb{N}$. Houghton's group $H_n$ is the group of permutations of $\{1,\dots, n\}\times \mathbb{N}$, that eventually act as a translation in each copy of $\mathbb{N}$. We prove the solvability of the conjugacy problem and…

We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…

We resolve the isomorphism problem for tensor algebras of unital multivariable dynamical systems. Specifically we show that unitary equivalence after a conjugation for multivariable dynamical systems is a complete invariant for complete…

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on…

We characterize the group property of being with infinite conjugacy classes (or icc, in which all conjugacy classes beside 1 are infinite) for extensions of some specific groups ; namely extensions of abelian, centerless, icc, or word…

There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or…

If $G_1$ and $G_2$ are torsion-free hyperbolic groups and $P<G_1\times G_2$ is a finitely generated subdirect product, then the conjugacy problem in $P$ is solvable if and only if there is a uniform algorithm to decide membership of the…

The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem…

Let V_* be the normalized unitary subgroup of the modular group algebra FG of a finite p-group G over a finite field F with the classical involution *. We investigate the isomorphism problem for the group V_*, that asks when the group V_*…

We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given…

We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…

This paper classifies the factorizations of almost simple groups with a factor having at least two nonsolvable composition factors. This together with a previous classification result of the authors reduces the factorization problem of…

In this paper, we prove results on the relationship between the complexity of the group and color isomorphism problems. The difficulty of color isomorphism problems is known to be closely linked to the the composition factors of the…

We establish several results on the word problem for just infinite groups. First, for finitely generated just infinite groups we show that the word problem is uniformly decidable for presentations with recursively enumerable sets of…

Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

In this paper we study the complexity of solving orientable quadratic equations in wreath products $A\wr B$ of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given…

If G and H are finitely generated, residually nilpotent metabelian groups, H is termed para-G if there is a homomorphism of G into H which induces an isomorphism between the corresponding terms of their lower central quotient groups. We…

We provide two alternative ways to determine the number of (bi-)twisted conjugacy classes in a finite group: one by counting certain irreducible characters and one by counting certain twisted conjugacy classes of other endomorphisms. In…