Related papers: Fundamental groups and presentations of algebras

We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.

We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$. We produce partial results for abelian varieties over a general finite…

In this paper we describe all group gradings by a finite abelian group G of any Lie algebra L of the type "A" over algebraically closed field F of characteristic zero.

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…

We know that any finite abelian group $G$ appears as a subgroup of infinitely many multiplicative groups $\mathbb{Z}_n^\times$ (the abelian groups of size $\phi(n)$ that are the multiplicative groups of units in the rings…

The complete algebraic structure of semisimple finite group algebra of a generalized strongly monomial group is provided. This work extends the work of Broche and del R{\'{\i}}o on strongly monomial groups. The theory is complimented by an…

Let $G$ be a group. The subsets $A_1,\ldots,A_k$ of $G$ form a complete factorization of group $G$ if if they are pairwise disjoint and each element $g\in G$ is uniquely represented as $g=a_1\ldots a_k$, with $a_i\in A_i$. We prove the…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

Let $G$ be a finite group and $Ch_i(G)$ some quantitative sets. In this paper we study the influence of $Ch_i(G)$ to the structure of $G$. We present a survey of author and his colleagues' recent works.

Let $G$ be an $\ell$-group (which is short for ``lattice-ordered abelian group''). Baker and Beynon proved that $G$ is finitely presented iff it is finitely generated and projective. In the category $\mathcal U$ of {\it unital}…

We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

In this paper we describe all group gradings by a finite abelian group $\Gamma$ of a simple Lie algebra of type $G_2$ over an algebraically closed field $F$ of characteristic 0.

Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…

The problem of classifying equivalence classes of presentations up to isomorphism of Cayley graphs is considered in this article in the case of dicyclic groups. The number of equivalence classes of presentations is uniformly bounded - it is…

We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine,…

In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.

We introduce the notion of a conjugation-free geometric presentation for a fundamental group of a line arrangement's complement, and we show that the fundamental groups of the following family of arrangements have a conjugation-free…