Archivo del Autor: Ramon ESTEBAN ROMERO

Defensa tesi doctoral Neus Fuster i Corral 28/07/2021, 11.00, sala graus «Manuel Valdivia»/en línia

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Jul ’21
28
11:00

El proper dijous 28 d’octubre de 2021, a les 11.00, a la sala de graus «Manuel Valdivia» de la Facultat de Ciències Matemàtiques de la Universitat de València (carrer del Doctor Moliner, 50, Burjassot), es procedirà a la defensa de la tesi doctoral de Neus Fuster i Corral, dirigida per Adolfo Ballester Bolinches i Ramon Esteban Romero i amb títol

«Left braces and the Yang-Baxter equation».

Esteu convidats a assistir a aquest acte, que podreu seguir presencialment o connectant-vos a https://links.uv.es/permut/tesiNeusFuster.

Paper «The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation» published in Mediterr. J. Math.

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A. Ballester-Bolinches, R. Esteban-Romero, N. Fuster-Corral, H. Meng.
The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation.
Mediterr. J. Math, 18: Article number 145, 2021.

doi: 10.1007/s00009-021-01793-7

Abstract:

We describe the left brace structure of the structure group and the permutation group associated with an involutive, non-degenerate set-theoretic solution of the quantum Yang–Baxter equation using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.

2020 Mathematics Subject Classification: 16T25, 05C25, 20F05, 20F65

Keywords: left brace, Yang-Baxter equation, Cayley graph, structure group.

Talk «On products of π-decomposable groups and Hall-like theorems» by Ana Martínez-Pastor at 2021 Zassenhaus Groups and Friends Conference, 04/06/2021, 15.15

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Jun ’21
4
15:15

Ana Martínez Pastor will give the talk «On products of π-decomposable groups and Hall-like theorems» at 2021 Zassenhaus Groups and Friends Conference, online, on 04/06/2021 at 15.15. More information:

https://www2.math.binghamton.edu/p/zassenhaus/zassenhaus_2021/home

Talk «On the computability of the abelian kernel of an inverse semigroup» by Vicent Pérez-Calabuig at 2021 Zassenhaus Groups and Friends Conference, 28/05/2021, 15.50

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May ’21
28
15:50

Vicent Pérez-Calabuig will give the talk «On the computability of the abelian kernel of an inverse semigroup» at 2021 Zassenhaus Groups and Friends Conference, online, on 28/05/2021 at 15.50. More information:

https://www2.math.binghamton.edu/p/zassenhaus/zassenhaus_2021/home

Poster presentation «An approach to skew left braces via triply factorised groups», Ramón Esteban-Romero, Ischia Group Theory 2020/2021, 26/03/2021, 09.55

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Mar ’21
26
9:55

Ramón Esteban Romero will present his poster «An approach to skew left braces via triply factorised groups» in Ischia Group Theory 2020/2021, online, on 26/03/2021, from 09.55 to 10.00. More information:

http://www.dipmat2.unisa.it/ischiagrouptheory/agenda_2021.html

Xarrada «Les màquines del llenguatge» d’Enric Cosme Llópez a la Setmana Cultural de la Facultat de Ciències Matemàtiques, 18/03/2021, 12.00

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Mar ’21
18
11:00

Enric Cosme Llópez presentarà la xarrada «Les màquines del llenguatge» el dia 18/03/2021 a les 12.00 dins del programa d’activitats de la Setmana Cultural de Matemàtiques 2021.

https://www.uv.es/coslloen/Arxiu/Fitxers/Beamers/UV21.pdf

Paper «Thompson-like characterization of solubility for products of finite groups» published in Ann. Mat. Pura Appl. (4)

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P. Hauck, L. S. Kazarin, A. Martínez-Pastor, and M. D. Pérez-Ramos.
Thompson-like characterization of solubility for products of finite groups.
Ann. Mat. Pura Appl. (4), 200(1):337–362, 2021.

doi:10.1007/s10231-020-00998-z

Abstract

A remarkable result of Thompson states that a finite group is soluble if and only if all its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory of groups, aiming for global properties of groups from local properties of two-generated (or more generally, n-generated) subgroups. We contribute an extension of Thompson’s theorem from the perspective of factorized groups. More precisely, we study finite groups G = AB with subgroups A, B such that ⟨a, b⟩ is soluble for all a ∈ A and b ∈ B. In this case, the group G is said to be an S-connected product of the subgroups A and B for the class S of all finite soluble groups. Our Main Theorem states that G = AB is S-connected if and only if [A, B] is soluble. In the course of the proof, we derive a result about independent primes regarding the soluble graph of almost simple groups that might be interesting in its own right.

2020 Mathematics Subject Classification: 20D40, 20D10

Keywords: Solubility, products of subgroups, two-generated subgroups, S-connection, almost simple groups, independent primes

Paper «On finite involutive Yang-Baxter groups» published in Proc. Amer. Math. Soc.

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H. Meng, A. Ballester-Bolinches, R. Esteban-Romero, and N. Fuster-Corral.
On finite involutive Yang-Baxter groups.
Proc. Amer. Math. Soc., 149(2):793–804, 2021.

doi:10.1090/proc/15283

Abstract

A group G is said to be an involutive Yang-Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, nondegenerate set-theoretic solution of the Yang-Baxter equation. We give new sufficient conditions for a group that can be factorised as a product of two IYB-groups to be an IYB-group. Some earlier results are direct consequences of our main theorem.

2020 Mathematics Subject Classification: Primary 81R50; Secondary 20F29, 20B35, 20F16, 20C05, 16S34, 16T25

Keywords: Finite left brace, Yang-Baxter equation, involutive nondegenerate solutions, involutive Yang-Baxter group

Charla de Ana Martínez Pastor en «Finite groups in Valencia», 30/03/2021, 17.40

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Mar ’21
30
17:40

El próximo 30 de marzo de 2021 de 17.40 a 18.25, Ana Martínez Pastor pronunciará la charla «Hall-like theorems in products of π-decomposable groups» en el congreso Finite groups in Valencia. Más información en

https://sites.google.com/view/finite-groups-seminar2021/

Paper «On finite p-groups of supersoluble type» published in J. Algebra

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The following paper has been published:
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El següent article ha sigut publicat:

A. Ballester-Bolinches, R. Esteban-Romero, H. Meng, and N. Su.
On finite p-groups of supersoluble type.
J. Algebra, 567:1–10, 2021.

doi:10.1016/j.jalgebra.2020.08.025

Abstract

A finite p-group S is said to be of supersoluble type if every fusion system over S is supersoluble. The main aim of this paper is to characterise the finite p-groups of supersoluble type. Abelian and metacyclic p-groups of supersoluble type are completely described. Furthermore, we show that the Sylow p-subgroups of supersoluble type of a finite simple group must be cyclic.

2020 Mathematics Subject Classification: 20D20; 20D15; 20D05

Keywords: finite group; fusion system; supersolubility