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

Nov ’20

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


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

– You are welcome to share the Zoom link with other interested

– 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
( 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 (

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


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:

Talk «Thompson-like characterization of solubility for products of groups» at 2020 Zassenhaus Groups and Friends Conference

May ’20

María Dolores Pérez Ramos will give the talk entitled

Thompson-like characterization of solubility for products of groups

at the 2020 Zassenhaus Groups and Friends Conference online on 29th May 2020 at 15.55. The link for the talk and its recording appear on


A remarkable result of Thompson states that a finite group is soluble if
and only if its two-generated subgroups are soluble. This result has been
sharply generalized, and it is in the core of a wide area of study in the theory
of groups, aiming for global properties of groups from local properties of two-
generated (or more generally, n-generated) subgroups. We report about an
extension of Thompson’s theorem from the perspective of factorized groups.
We prove that for a finite group G = AB, with A, B subgroups of G, if ha, bi
is soluble for all a ∈ A and all b ∈ B, then [A, B] is soluble. In that 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. As an application, deep results about
connected products of finite soluble groups, for other relevant classes of
groups, are extended to the finite universe. Collaboration with M. P. Gállego (U.
Zaragoza, Spain), P. Hauck (U. Tübingen, Germany), L. Kazarin (U. Yaroslavl,
Russia), A. Martı́nez-Pastor (U. Politècnica de València, Spain) .

Visita i xarrada professor Jean-Éric Pin 24/02/2020

Feb ’20

Jean-Éric PinBenvolgudes companyes, benvolguts companys,

El professor Jean-Éric Pin (IRIF, CNRS i Université Paris-Diderot) ens visitarà el proper dilluns 24 de febrer i impartirà la xarrada

«Formations of monoids»

el proper dilluns 24 de febrer a les 12.00 a l’aula 1.5 de la Facultat de Matemàtiques.

Ben cordialment,


Seminaris Paola Stefanelli i Marzia Mazzotta 30/10/2019 16.30

Oct ’19

Benvolgudes companyes, benvolguts companys,

El proper dimecres 30 d’octubre, a partir de les 16.30 hores, al seminari d’Àlgebra de la Facultat de Matemàtiques de la Universitat de València (2n pis) es duran a terme els següents seminaris:

  • 16.30 Paola Stefanelli (Università del Salento, Lecce, Pulla, Itàlia) «Set-theoretical solutions to the Yang-Baxter equation of finite order» (resum)
  • 17.00 Marzia Mazzotta (Università del Salento, Lecce, Pulla, Itàlia) «Recent developments of the pentagon equation with an application to the Yang-Baxter equation» (resum)

Us convidem a assistir-hi.

Conferencia Arnold D. Feldman 16/04/2019

Abr ’19

El próximo martes 16 de abril a las 12.00h en el Seminario del IUMPA (UPV) el profesor Arnold Feldman, del Franklin & Marshall College (Lancaster, PA, EEUU), impartirá una conferencia titulada «Analogues of pronormality in $\sigma$-solvable finite groups». Estáis todos invitados.

This is a preliminary talk about topics in finite groups that I am discussing with M.D. Pérez-Ramos and Rex Dark. Skiba and others have studied a generalization of solvability that they call σ-solvability, where σ is a partition of the set of prime integers. When σ is the partition in which each set contains exactly one prime, σ-solvability is just solvability. Many properties of solvable groups and their subgroups have analogues in σ-solvable groups. In this talk, we introduce two possible generalizations of pronormality, which we call σ-pronormality and weak σ-pronormality, and describe how they interact with other subgroup properties, including σ-subnormality as defined in Skiba’s work.

Charla «Teoría del endomorfismo, recurrencias lineales y ecuaciones diferenciales», Ramón Esteban Romero, jueves 19/04/2018, 13.00

Abr ’18

Dijous 19/04/2018, a les 13.00, a la sala «Charles Darwin» del campus de Burjassot (Facultat de Farmàcia) impartiré la xarrada amb títol «Teoria de l’endomorfisme, recurrències lineals i equacions diferencials», dins del cicle de conferències dels seminaris de les assignatures de segon i tercer del grau de Matemàtiques.

Esteu tots convidats.

El jueves 19/04/2018, a las 13.00, en la sala «Charles Darwin» del campus de Burjassot (Facultat de Farmàcia) impartiré la charla titulada «Teoría del endomorfismo, recurrencias lineales y ecuaciones diferenciales», dentro del ciclo de conferencias de los seminarios de las asignaturas de segundo y tercero del grado de Matemáticas.

Estáis todos invitados.

Visita del profesor Jorge Almeida (31/08-07/09/2016)

Ago ’16Sep

Estimados compañeros, estimadas compañeras:

El profesor Jorge Almeida (Universidade do Porto, Portugal) visitará el Departament de Matemàtiques entre el 31 de agosto y el 7 de septiembre de 2016. Es experto en teoría de semigrupos, autómatas y lenguajes formales. Durante su estancia impartirá dos charlas:

  • Viernes 2 de septiembre, 12.00 h
    Seminario del Instituto Universitario de Matemática Pura y Aplicada
    Universitat Politècnica de València
    «Recent progress on concatenation hierarchies of star-free languages»
    A celebrated theorem of Schützenberger (1965) states that a language can be expressed in the letters using only finite union, complementation, and concatenation (the so-called star-free languages) if and only if its syntactic semigroup has only trivial subgroups. On the other hand, McNaughton and Papert (1971) showed that such languages are precisely those that may be defined by first order sentences, where words are viewed as finite linear orders with predicates for each letter to express that the letter appears in a specific position. The combination of the two theorems provides an algorithm to decide when a regular language admits such a definition. A further ingredient was given by W. Thomas (1982), who showed that the analogue of the arithmetical hierarchy in this context, determined by the alternation of quantifiers, is intimately connected with the alternation of the closures under union, intersection, and concatenation, versus union and complementation, a hierarchy first introduced by Brzozowski (1971). The major open problem in this area is whether one can compute the minimum number of quantifier alternations needed to define a given star-free language. The purpose of the talk is to survey recent progress on this topic.
  • Martes 6 de septiembre, 12.00 h
    Seminario de Álgebra, Departament de Matemàtiques
    Universitat de València
    «Rauzy graphs and the free profinite semigroup»
    Symbolic dynamical systems have been studied from many viewpoints, in particular in an attempt to classify them. Several algebraic and combinatorial structures have been associated to them. In the case of minimal systems, we have established a relationship between Rauzy graphs, which describe the successive reading of blocks of symbols of fixed length and certain profinite subgroups of the free profinite semigroup on the underlying set of symbols. More precisely, we have shown that these groups may be obtained as inverse limits of the profinite completions of the fundamental groups of the Rauzy graphs as the length of the blocks varies. This is joint work with Alfredo Costa (University of Coimbra).




Visita y charla del profesor Gil Kaplan

May ’14May
May ’14

El profesor Gil Kaplan, de la School of Computer Science del Academic College of Tel Aviv-Yafo (Israel), visitará el Departament d’Àlgebra de la Universitat de València entre los días 26 y 29 de mayo de 2014. El profesor Kaplan es especialista en teoría abstracta de grupos finitos.

El martes 27 de mayo, a las 11.30, impartirá la charla titulada

Nilpotency, solvability and the twisting function of finite groups

en el seminario del Departament d’Àlgebra de la Universitat de València (segundo piso de la Facultat de Matemàtiques). Estáis todos invitados.


Charla de Paz Jiménez «Clases de isomorfía de transversales (quasigrupos)» 26/02/2014 11.00

Feb ’14

Paz Jiménez SeralLa profesor Paz Jiménez Seral, de la Universidad de Zaragoza, impartirá el próximo miércoles 26 de febrero de 2014, a las 11.00, la charla titulada

«Clases de isomorfía de transversales (quasigrupos)»

en el seminario del Departament d’Àlgebra de la Universitat de València (Facultat de Matemàtiques, segunda planta).

Estáis todos invitados.

Más información sobre Paz Jiménez Seral en la entrada


Charla de Ramón Esteban «Cómo usar las matemáticas para comunicarnos» martes 11/02 18.00 en La Nau Gran

Feb ’14

El próximo martes 11 de febrero de 2014, a las 18.00, en la sala de actos «Charles Darwin» del aulario del campus de Burjassot, Ramón Esteban impartirá la charla titulada

«Cómo usar las matemáticas para comunicarnos»

como parte del 12º ciclo de conferencias «Temas de actualidad en Ciencias» de «La nau Gran», el programa universitario de la Universitat de València para mayores de 55 años. Estáis invitados a asistir.

Nota: Esta charla estaba prevista originalmente para el 8 de abril.


En esta charla veremos algunos problemas que se pueden dar en el ámbito de la comunicación y cómo las matemáticas pueden ayudarnos a resolverlos. En concreto, uno de los problemas es el ruido puede producir errores en la transmisión de información que es necesario corregir o, al menos, detectar. Este es el objeto de la llamada teoría de códigos. Los dígitos o caracteres de control constituyen un mecanismo para mitigar el efecto de esos errores. La aritmética modular o aritmética del reloj nos permite diseñar sistemas de dígitos de control que nos sirven para detectar o corregir errores. Por otra parte, hay ocasiones en que interesa mantener en secreto alguna comunicación a salvo de terceras personas. Para ello, es necesario cifrarlo de modo que si alguien lo intercepta, no pueda entenderlo. De nuevo, la aritmética del reloj resulta ser una potente herramienta matemática que está en la base del diseño de muchos sistemas criptográficos. Durante la charla presentaremos las nociones básicas de la teoría de códigos y de la criptografía y mostraremos algunos ejemplos de dígitos de control y de sistemas criptográficos basados en la aritmética modular.