Related papers: Applications of computational tools for finitely p…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n,…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
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 paper discusses issues related to the use of faceted classifications in an online environment. The author argues that knowledge organization systems can be fully utilized in information retrieval only if they are exposed and made…
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
Complex real-world networks commonly reveal characteristic groups of nodes like communities and modules. These are of value in various applications, especially in the case of large social and information networks. However, while numerous…
Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…
To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
We introduce the concept of quantifying the extent to which a finitely generated group is residually finite. The quantification is carried out for some examples including free groups, the first Grigorchuk group, finitely generated nilpotent…
We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…
In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…
In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
We study the problem of deciding whether or not the image of an irreducible representation of the braid group $\B_3$ of degree $\leq 5$ has finite image if we are only given the eigenvalues of a generator. We provide a partial algorithm…
We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.
We consider pairs of finitely presented, residually finite groups $P\hookrightarrow\G$ for which the induced map of profinite completions $\hat P\to \hat\G$ is an isomorphism. We prove that there is no algorithm that, given an arbitrary…