Related papers: Calculating Subgroups with GAP
The subgroup pattern of a finite groups $G$ is the table of marks of $G$ together with a list of representatives of the conjugacy classes of subgroups of $G$. In this article we present an algorithm for the computation of the subgroup…
We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d\times d$ matrices over a finite field $\mathbb{F}_q$, known to be isomorphic…
This contains a new version of the so-called non-commutative Gauss algorithm for polycyclic groups. Its results allow to read off the order and the index of a subgroup in an (possibly infinite) polycyclic group.
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients.
We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.
We present an algorithm to explore various properties of the numerical semigroups with a given maximum primitive. In particular, we count the number of such numerical semigroups and verify that there is no counterexample to Wilf's…
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. It turns out that Stallings'…
A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.
We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The…
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…
We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
In this paper, we describe an algorithm for computing the left, right, or 2-sided congruences of a finitely presented semigroup or monoid with finitely many classes, and an alternative algorithm when the finitely presented semigroup or…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…