Related papers: Calculating Subgroups with GAP

In scenarios that require teamwork, we usually have at hand a variety of specific tasks, for which we need to form a team in order to carry out each one. Here we target the problem of matching teams with tasks within the context of…

We present a new algorithm to decide finiteness of matrix groups defined over a field of positive characteristic. Together with previous work for groups in zero characteristic, this provides the first complete solution of the finiteness…

We present a family of algorithms for computing the Galois group of a polynomial defined over a $p$-adic field. Apart from the "naive" algorithm, these are the first general algorithms for this task. As an application, we compute the Galois…

The article demonstrates the procedure how to compute the Zariski closure of an orbit by an algebraic action of finitely generated group on the affine plane. First half of the algorithm is about deciding whether given finitely generated…

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…

This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.

In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an algorithm for computing all Arf special gaps of a given Arf numerical semigroup. We introduce the concept of Arf-irreducible numerical…

In this notes we give details of the proofs performed with GAP of the theorems of our paper "Pointed Hopf Algebras over the Sporadic Simple Groups".

We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…

The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…

The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…

In this paper, we define the notion of crossed modules of groups with action and investigate related structures. Functions for computing of these structures have been written using the GAP computational discrete algebra programming…

We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer.

In the theory of algebraic groups, parabolic subgroups form a crucial building block in the structural studies. In the case of general linear groups over a finite field $F_q$, given a sequence of positive integers $n_1, ..., n_k$, where…

Let $G$ be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of $G$ and a bound on the Pr\"{u}fer rank of $G$. This yields in turn an algorithm to decide whether a finitely…

The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…

We determine all groups definable in Presburger arithmetic, up to a finite index subgroup.

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $\mathcal{M}_{\sigma}$ of a compact closed surface $X$ of genus $\sigma$ is considered. A complete method of enumeration is achieved for…

We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem…