Paper «Large characteristically simple sections of finite groups» published in Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. (RACSAM)

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A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral
Large characteristically simple sections of finite groups.
Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. (RACSAM), 116, Article number 41, 2022.

doi: 10.1007/s13398-021-01188-z

Abstract:

In this paper we prove that if G is a group for which there are k non-Frattini chief factors isomorphic to a characteristically simple group A, then G has a normal section C/R that is the direct product of k minimal normal subgroups of G/R isomorphic to A. This is a significant extension of the notion of crown for isomorphic chief factors.

2020 Mathematics Subject Classification: 20E34, 20E28, 20D10, 20P05.

Keywords: finite group, maximal subgroup, probabilistic generation, primitive group, crown.

Charla «Grupos, brazas y la ecuación de Yang-Baxter» de Ramón Esteban Romero en el Seminario GRACIA-RedMat

Nov ’21
3
17:00

Título: Grupos, brazas y la ecuación de Yang-Baxter
Expositor: Ramón Esteban Romero 
Institución: Universitat de València
Fecha:  miércoles 03 de noviembre de  2021 entre 11:00 y 12:00 AM (hora Dominicana) (17:00 hora española)

sesión zoomhttps://reuna.zoom.us/j/89895566542?pwd=VzFGNTVzQ1dzbHA0Ujh4cTRmU1Vsdz09
ID de reunión: 898 9556 6542
Código de acceso: 092266

Estamos en YouTubeCanal de YouTube

anuncio: archivo adjunto

https://permut.blogs.uv.es/files/2022/01/Esteban-R.pdf

_______________________

Primitivo B. Acosta-Humánez

Coordinador Red Matemática

Grupos, Álgebras, Relatividad, Combinatoria, Integrabilidad y Aritmética

Charla «Cómo usar las matemáticas para resolver el cubo de Rubik» por Ramón Esteban Romero, Universidad de Almería, 08/10/2021, 11.30-12.45

Oct ’21
8
11:30

Póster INDALMAT 2021

CONFERENCIA: Cómo usar las matemáticas para resolver el cubo de Rubik.

Ponente: Ramón Esteban Romero. Departament de Matemàtiques Facultat de Ciències Matemàtiques (Universitat de València)
Con la colaboración de: Óscar Roldán Blay. Departamento de Análisis Matemático (Universitat de València)

Esta charla forma parte del VI Concurso INDALMAT de resolución de problemas de matemáticas.

http://www.ualjoven.ual.es/index.php/actividades/69-concurso-indalmat-de-resolucion-de-problemas-de-matematicas

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

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.

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

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.

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

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

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

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

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

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

The following paper has been published:
El siguiente artículo ha sido publicado:
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

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

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

A. Ballester-Bolinches, R. Esteban-Romero, H. Meng, N. Su
On certain products of permutable subgroups.
J. Algebra, 567, 1-10.

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

Talk «Triply factorised groups and skew left braces» at Ischia Online Group Theory Conference (GOThIC) on 19th November, 2020

Nov ’20
19
17:00

The organising committee of the
Ischia Online Group Theory Conference(GOThIC)
is inviting you to a scheduled Zoom meeting.

PLEASE NOTE:

– The TIME OF THE TALK is 17:00 CET = UTC + 1.

– You are welcome to share the Zoom link with other interested
parties, but PLEASE DO NOT POST THE LINK PUBLICLY.

– When joining, please MAKE SURE THAT YOUR NICKNAME
IS YOUR NAME AND SURNAME, or close to it, so that the organisers
can recognise you and let you in

The Ischia Group Theory 2020 Conference
(http://www.dipmat2.unisa.it/ischiagrouptheory/) was planned
for 30 March – 4 April 2020. It has now been postponed.
In the meantime, we are offering a series of online lectures
by leading researchers (https://sites.google.com/unisa.it/e-igt2020/).

TIME: November 19th, 2020 17:00 CET (UTC+1)

COFFEE BREAK: The talk will start at 17:00 CET. The conference room
will open at 16:45 CET for a coffee break
– Bring Your Own tea/coffee mug – biscuits appreciated –
and join us for some smalltalk before the event.

SPEAKER: Ramon Esteban-Romero (Universitat de València)

TITLE: Triply factorised groups and skew left braces

ABSTRACT:

The Yang-Baxter equation is a consistency equation of the statistical mechanics proposed by Yang [6] and Baxter [1] that describes the interaction of many particles in some scattering situations. This equation lays the foundation for the theory of quantum groups and Hopf algebras. During the last years, the study suggested by Drinfeld [2] of the so-called set-theoretic solutions of the Yang-Baxter equation has motivated the appearance of many algebraic structures. Among these structures we find the skew left braces, in troduced by Guarnieri and Vendramin [3] as a generalisation of the structure of left brace defined by Rump [4]. It consists of a set B with two operations + and ·, not necessarily commutative, that give B two structures of group linked by a modified distributive law.

The multiplicative group C = (B, ·) of a skew left brace (B, +, ·) acts on the multiplicative group K = (B, +) by means of an action λ: C −→ Aut(K) given by λ(a)(b) = −a + a · b, for a, b ∈ B. With respect to this action, the identity map δ : C −→ K becomes a derivation or 1-cocycle with respect to λ. In the semidirect product G = [K]C = {(k, c) | k ∈ K, c ∈ C}, there is a diagonal-type subgroup D = {(δ(c), c) | c ∈ C} such that G = KD = CD, K ∩ D = C ∩ D = 1. This approach was presented by Sysak in [5] and motivates the use of techniques of group theory to study skew left braces.

We present in this talk some applications of this approach to obtain some results about skew left braces. These results have been obtained in collaboration with Adolfo Ballester-Bolinches.

Recorded talks: https://sites.google.com/unisa.it/e-igt2020/recorded-talks