Minimal Presentations

2016 ◽  
pp. 69-83
Author(s):  
Abdallah Assi ◽  
Pedro A. García-Sánchez
Keyword(s):  
Minimal Presentations

Minimal presentations for groups of order 2n, n ≤ 6

1973 ◽  
Vol 15 (4) ◽  
pp. 461-469 ◽  
Author(s):  
T. W. Saga ◽  
J. W. Wamsley
Keyword(s):  
Generating Set ◽  
Image Position ◽  
Minimal Presentations ◽  
Minimal Generating Set

Let G be a finite 2-group having a minimal generating set {x1, …, xr} so that r = d (G) is an invariant of G. Suppose further that G has a presentation then.

scholarly journals PROFINITE COMPLETION OF GRIGORCHUK'S GROUP IS NOT FINITELY PRESENTED

2012 ◽  
Vol 22 (05) ◽  
pp. 1250045
Author(s):  
MUSTAFA GÖKHAN BENLI
Keyword(s):  
Profinite Group ◽  
Profinite Completion ◽  
Infinite Dimensional ◽  
Grigorchuk Group ◽  
Schur Multipliers ◽  
Finite Quotients ◽  
Minimal Presentations ◽  
Finitely Presented

In this paper we prove that the profinite completion [Formula: see text] of the Grigorchuk group [Formula: see text] is not finitely presented as a profinite group. We obtain this result by showing that [Formula: see text] is infinite dimensional. Also several results are proven about the finite quotients [Formula: see text] including minimal presentations and Schur Multipliers.

scholarly journals Isolated factorizations and their applications in simplicial affine semigroups

2019 ◽  
Vol 19 (05) ◽  
pp. 2050082 ◽  
Author(s):  
Pedro A. García-Sánchez ◽  
Andrés Herrera-Poyatos
Keyword(s):  
Complete Intersection ◽  
Minimal Element ◽  
Numerical Semigroups ◽  
Commutative Monoid ◽  
Generalize Formula ◽  
Affine Semigroups ◽  
Minimal Presentations ◽  
Minimal Generators

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups. We also generalize [Formula: see text]-rectangular numerical semigroups to the context of simplicial affine semigroups and study their isolated factorizations. As a consequence of our results, we characterize those complete intersection simplicial affine semigroups with only one Betti minimal element in several ways. Moreover, we define Betti sorted and Betti divisible simplicial affine semigroups and characterize them in terms of gluings and their minimal presentations. Finally, we determine all the Betti divisible numerical semigroups, which turn out to be those numerical semigroups that are free for any arrangement of their minimal generators.

scholarly journals Strongly Peaking Representations and Compressions of Operator Systems

2020 ◽  
Author(s):  
Kenneth R Davidson ◽  
Benjamin Passer
Keyword(s):  
Convex Sets ◽  
Uniqueness Theorems ◽  
Unitary Equivalence ◽  
Operator System ◽  
Direct Sum ◽  
Operator Systems ◽  
Minimal Presentations ◽  
Minimality Conditions ◽  
Additional Assumptions

Abstract We use Arveson’s notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets that admit minimal presentations. A fully compressed separable operator system necessarily generates the $C^*$-envelope and is such that the identity is the direct sum of strongly peaking representations. In particular, a fully compressed presentation of a separable operator system is unique up to unitary equivalence. Under various additional assumptions, minimality conditions are sufficient to determine a separable operator system uniquely.

scholarly journals ON PRESENTATIONS OF COMMUTATIVE MONOIDS

1999 ◽  
Vol 09 (05) ◽  
pp. 539-553 ◽  
Author(s):  
J. C. ROSALES ◽  
P. A. GARCÍA-SÁNCHEZ ◽  
J. M. URBANO-BLANCO
Keyword(s):  
Commutative Monoid ◽  
Commutative Monoids ◽  
Minimal Presentations

In this paper, we introduce the concept of a strongly reduced monoid and we characterize the minimal presentations for such monoids. As a consequence, we give a method to obtain a presentation for any commutative monoid.

scholarly journals Minimal Presentations of Full Subsemigroups of ${\bf N}^2$

2001 ◽  
Vol 31 (4) ◽  
pp. 1417-1422
Author(s):  
J.C. Rosales ◽  
P.A. García-Sánchez
Keyword(s):  
Minimal Presentations

Minimal presentations for irreducible sofic shifts

1994 ◽  
Vol 40 (6) ◽  
pp. 1818-1825 ◽  
Author(s):  
N. Jonoska ◽  
B. Marcus
Keyword(s):  
Sofic Shifts ◽  
Minimal Presentations

scholarly journals Presentations of a numerical semigroup

2020 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Belgin Özer ◽  
Sibel Kanbay
Keyword(s):  
Complete Intersection ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Catenary Degree ◽  
Minimal Presentations

In this paper, we mainly study the minimal presentations of numerical semigroups. Moreover, we examine the concept of gluing, complete intersection, catenary degree, elasticity of some numerical semigroups.  

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