Paper «On σ-subnormality criteria in finite groups» published in J. Pure Appl. Algebra

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A. Ballester-Bolinches, S. F. Kamornikov, X. Yi.
On σ-subnormality criteria in finite groups.
J. Pure Appl. Algebra, 226(2):106822, 2022.

doi: 10.1016/j.jpaa.2021.106822

Abstract:

Let σ={σ_i: i∈ I} be a partition of the set P of all prime numbers. A subgroup H of a finite group G is called σ-subnormal in G if there is a chain of subgroups H= H_0⊆ H_1⊆⋯⊆ H_n= G where, for every i= 1,…, n, H_{i− 1} normal in H i or H i/Core_{H_i} (H_{i− 1}) is a σ_j-group for some j∈ I. In the special case that σ is the partition of P into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. In this paper some σ-subnormality criteria for subgroups of finite groups are studied.

2020 Mathematics Subject Classification: 20D10, 20D20.

Keywords: finite group, σ-nilpotency, σ-subnormal subgroup.

Paper «Generalised mutually permutable products and saturated formations» published in J. Algebra

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A. Ballester-Bolinches, S. Y. Madanha, M. C. Pedraza-Aguilera.
Generalised mutually permutable products and saturated formations.
J. Algebra, 595:434-443, 2022.

doi: 10.1016/j.jalgebra.2021.12.027

Abstract:

We say that a group G = AB is the weakly mutually permutable product of the subgroups A and B, if A permutes with every subgroup of B containing AB and B permutes with every subgroup of A containing AB. We prove that some known results for mutually permutable products remain true for weakly mutually permutable ones. Moreover, if G‘ is nilpotent, A permutes with every Sylow subgroup of B and B permutes with every Sylow subgroup of A, we show that G^F = A^FB^F, where is F a saturated formation containing U, the class of supersoluble groups. This generalises the corresponding result on mutually permutable products.

2020 Mathematics Subject Classification: 20D10, 20D20.

Keywords: weakly mutually permutable products, saturated formations, residuals

Paper «Nilpotent length and system permutability» published in J. Algebra

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Rex Darl, Arnold D. Feldman, M. D. Pérez-Ramos.
Nilpotent length and system permutability.
J. Algebra, 589:287-322, 2022.

Abstract:

If C is a class of groups, a C-injector of a finite group G is a subgroup V of G with the property that VK is a C-maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F-injectors in finite soluble groups for Fitting classes F. We shall show that for groups of nilpotent length at most 4, F-injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible.

2020 Mathematics Subject Classification: 20D10, 20D20.

Keywords: Fitting soluble group, Fitting class, injector, system permutability.

Talk «Carter and Gaschütz theories revisited» by María Dolores Pérez-Ramos at Ischia Online Group Theory Conference (GOThIC), 09/12/2021, 18.00

Dic ’21
9
18:00

The Organizing 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 18:00 CET (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 ANDSURNAME, or  close to it, so  that the organisers can recognise you and let you in.
TOPIC: GOThIC – Ischia Online Group Theory Conference –  (https://sites.google.com/unisa.it/e-igt2020/).
TIME: Thursday December 9th, 2021 18:00 CET (UTC+1). 
COFFEE BREAK: The  talk will start at 18:00 CET.  The conference roomwill open at 17:45 CET for a drink – Bring Your Own appropriate drink – biscuits appreciated – and join us for some smalltalk before the event.
SPEAKER: Maria Dolores Pérez -Ramos (Universitat de València)
TITLE: Carter and Gaschütz theories revisited

ABSTRACT: Classical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent subgroups, coincide with nilpotent projectors and with nilpotent covering subgroups, and they form a non-empty conjugacy class of subgroups, in soluble groups. We present an extension of these facts to π-separable groups, for sets of primes π, by proving the existence of a conjugacy class of subgroups in π-separable groups, which specialize to Carter subgroups within the universe of soluble groups.

The approach runs parallel to the extension of Hall theory from soluble to π-separable groups by Cunihin, regarding existence and properties of Hall subgroups. Our Carter-like subgroups enable an extension of the existence and conjugacy of injectors associated to Fitting classes to π-separable groups, in the spirit of the role of Carter subgroups in the theory of soluble groups. This is joint work with M. Arroyo-Jordá, P. Arroyo-Jordá, R. Dark and A.D. Feldman.

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

Paper «A positive extension of Eilenberg’s variety theorem for non-regular languages» published in Appl. Algebra Eng. Commun. Comp.

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A. Cano, J. Cantero, A. Martínez-Pastor.
A positive extension of Eilenberg’s variety theorem for non-regular languages.
Appl. Algebra Eng. Commun. Comp., 32:553-573, 2021.

doi: 10.1007/s00200-020-00414-2

Abstract:

In this paper we go further with the study initiated by Behle, Krebs and Reifferscheid (in: Proceedings CAI 2011, Lecture Notes in Computer Science, vol 6742, pp 97–114, 2011), who gave an Eilenberg-type theorem for non-regular languages via typed monoids. We provide a new extension of that result, inspired by the one carried out by Pin in the regular case in 1995, who considered classes of languages not necessarily closed under complement. We introduce the so-called positively typed monoids, and give a correspondence between varieties of such algebraic structures and positive varieties of possibly non-regular languages. We also prove a similar result for classes of languages with weaker closure properties.

2020 Mathematics Subject Classification: 68Q70, 68Q45, 20M07, 20M35.

Keywords: monoids, varieties, formal languages.

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

Paper «A Note on a Paper of Aivazidis, Safonova and Skiba» published in Mediterr. J. Math.

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M. M. Al-Shomrani, Adolfo Ballester-Bolinches, A. A. Heliel.
A Note on a Paper of Aivazidis, Safonova and Skiba.
Mediterr. J. Math, 18: Article number 213, 2021.

doi: 10.1007/s00009-021-01872-9

Abstract:

The main result of this paper states that if F is a subgroup-closed saturated formation of full characteristic, then the F-residual of a K-F-subnormal subgroup S of a finite group G is a large subgroup of G provided that the F-hypercentre of every subgroup X of G containing S is contained in the F-residual of X. This extends a recent result of Aivazidis, Safonova and Skiba.

2020 Mathematics Subject Classification: 20D10, 20D20.

Keywords: finite group, saturated formation, K-F-subnormal subgroup.

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.