Results 1 to 10 of about 30,482 (215)
PRESENTATIONS OF AFFINE KAC–MOODY GROUPS [PDF]
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 +2 more
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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 Topological Full Groups by Generators and Relations [PDF]
, 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 +1 more
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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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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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Iterated Monodromy Groups of Quadratic Polynomials, I [PDF]
, 2008 We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the `kneading sequence' of the polynomial.
Bartholdi, Laurent +1 more
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The infinite simple group V of Richard J. Thompson : presentations by permutations [PDF]
, 2017 We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions ...
Bleak, Collin, Quick, Martyn
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Presenting a Category Modulo a Rewriting System [PDF]
, 2015 Presentations of categories are a well-known algebraic tool to provide descriptions of categories by the means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the
Clerc, Florence, Mimram, Samuel
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Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists [PDF]
, 2020 We give a method to compute presentations of saturated cluster modular groups. Using this, we obtain finite presentations of the saturated cluster modular groups of finite mutation type $X_6$ and $X_7$. We verify that the cluster modular groups of finite
Ishibashi, Tsukasa
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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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