Results 1 to 10 of about 383 (94)

On Efficient Presentations of the Groups PSL $(2, m)$ [PDF]

International Journal of Group Theory, 2022
We exhibit presentations of the Von Dyck groups $D(2, 3, m), \ m\ge 3$, in terms of two generators of order $m$ satisfying three relations, one of which is Artin's braid relation. By dropping the relation which fixes the order of the generators we obtain
Orlin Stoytchev
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Coherent Presentations of Monoidal Categories [PDF]

Logical Methods in Computer Science, 2017
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms.
Pierre-Louis Curien, Samuel Mimram
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PRESENTATIONS OF AFFINE KAC–MOODY GROUPS

Forum of Mathematics, Sigma, 2018
How many generators and relations does $\text{SL}\,_{n}(\mathbb{F}_{q}[t,t^{-1}])$ need? In this paper we exhibit its explicit presentation with $9$ generators and $44$ relations. We investigate presentations of affine Kac–Moody groups over finite fields.
INNA CAPDEBOSCQ, KARINA KIRKINA, DMITRIY RUMYNIN   +2 more
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Presentations of topological full groups by generators and relations

Journal of Algebra, 2018
Let \((\Omega,T)\) be a minimal subshift over a finite alphabet: \(\Omega\) is a closed subset of \(X^{\mathbb Z}\) for a finite alphabet \(X\), invariant under the shift map \(T\), and minimal under these conditions. The associated \textit{topological full group} is the group of self-homeomorphisms of \(\Omega\) that are piecewise powers of \(T\).
Grigorchuk, Rostislav, Medynets, Kostya
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The (CO)homology of groups given by presentations in which each defining relator involves at most two types of generators [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1992
AbstractOur set-up will consist of the following: (i) a graph with vertex set V and edge set E; (ii) for each vertex ∈ V a non-trivial group Gv given by a presentation (xν; rν); (iii) for each edge e = {u, ν} ∈ E a group Ge given by a presentation (xu, xv; re) where re consists of the elements of ru ∪ rv, together with some further words on xu ∪ xv. We
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Presentations of Topological Full Groups by Generators and Relations

, 2015
We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying subshift is recursive.
Grigorchuk, Rostislav, Medynets, Konstantin   +1 more
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Digraph Groups Without Leaf Having An Arc Count One Greater Than Their Vertex

Cumhuriyet Science Journal
This paper investigates a particular class of digraph groups that are defined by non-empty balanced presentations. Each relation is expressed in the form R(x,y), where x and y are distinct generators, and R(⋅,⋅) is based on a fixed cyclically reduced ...
Mehmet Sefa Cihan
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Finite groups defined by presentations in which each defining relator involves exactly two generators

Journal of Pure and Applied Algebra
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cihan, Mehmet Sefa, Williams, Gerald
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On presentations of K-groups by generators and relations

In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of bounded size suffice and we provide the corresponding relations.
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