Related papers: On integral extensions between the abelianization …

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…

For a certain class of abelian categories, we show how to make sense of the "Euler characteristic" of an infinite projective resolution (or, more generally, certain chain complexes that are only bounded above), by passing to a suitable…

For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions we construct a tower of interpolation categories. These are categories over which the functor factorizes and which capture…

While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…

We study an analogue of the conjugacy growth function in finitely generated groups: the automorphic growth function. This counts the number of automorphic orbits that intersect the ball of radius $n$ in the group. We show that this is not a…

In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a…

The goal of this thesis is to define a 2-dimensional version of abelian categories, where symmetric 2-groups play the role that abelian groups played in 1-dimensional algebra. Abelian and 2-abelian groupoid enriched categories are defined…

In this paper, we consider the formal power series whose n-th coefficient is the number of copies of a given finite graph in the ball of radius n centred at the identity element in the Cayley graph of a finitely generated group and call it…

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…

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…

This paper concerns exponential contravariant functors on free groups. We obtain an equivalence of categories between analytic, exponential contravariant functors on free groups and conilpotent cocommutative Hopf algebras. This result…

Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the…

We study the notion of fundamental group in the framework of descent-exact homological categories. This setting is sufficiently wide to include several categories of "algebraic" nature such as the almost abelian categories, the semi-abelian…

We develop methods for proving that certain extensions of polynomial functors do not split naturally. As an application we give a functorial description of the third and the fourth stable homotopy groups of the classifying spaces of free…

An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…

We construct a correspondence between the cohomology groups of a group $G$ relative to a family of subgroups $\famS$ and the classes of `relative extensions' of $G$ by abelian groups, modulo a certain equivalence relation. We establish this…

Extensive work has been done to determine necessary and sufficient conditions for a bijective correspondence of abelian extensions of number fields to force an isomorphism of the base fields. However, explicit examples of correspondences…

There are well known identities that involve the Ext bifunctor, coproducts, and products in Ab4 and Ab4* abelian categories with enough projectives and enough injectives. Namely, for every such category $\mathcal{A}$, the isomorphisms…

The work is devoted to the extension groups in the category of functors from a small category to an additive category with an Abelian structure in the sense of Heller. It is constructed a spectral sequence which converges to the extension…

In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper we address…