Related papers: Linear groups and computation
In recent years, there has been considerable success in computing Ext-groups of modular representations associated to the general linear group by relating this problem to one of computing Ext-groups in functor categories. In this paper, we…
We discuss various methods and their effectiveness for solving linear equations over finitely generated abelian groups. More precisely, if $\varphi\colon G\to H$ is a homomorphism of finitely generated abelian groups and $b\in H$, we…
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…
We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as well as in some other situations. This work relies in an…
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
This paper is a survey on the works [MS77, MS79, MS81] on maximal subgroups in finitely generated linear groups, and the works that followed it [GG08, GG13b, GG13a, Kap03, Iva92, HO16, GM16, AGS14, Sf90, Sf98, Per05, AKT16, FG18, GS17]…
We survey recent generalizations and improvements of the linear programming method that involve semidefinite programming. A general framework using group representations and tools from graph theory is provided.
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…
This expository article revolves around the question to find short presentations of finite simple groups. This subject is one of the most active research areas of group theory in recent times. We bring together several known results on…
Humans spend a significant part of their lives being a part of groups. In this document we propose research directions that would make it possible to computationally form productive groups. We bring to light several issues that need to be…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…
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…
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…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
We consider (projectively) linearly sofic groups, i.e. groups which can be approximated using (projective) matrices over arbitrary fields, as a generalization of sofic groups. We generalize known results for sofic groups and groups which…
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…
The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…