Ballester Bolinches, Adolfo; Cossey, John; Esteban Romero, Ramón(Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, 2009)
[EN] There are different ways to associate to a group a
certain graph. In this context, it is interesting to ask for the relations
between the structure of the group, given in group-theoretical
terms, and the structure ...
The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at ...
[EN] In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, ...
In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Ragland, Matthew F.(Walter de Gruyter, 2007-03)
[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, ...
We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is ...
[EN] In this note, we give an easy algorithm to construct the rational canonical form of a square matrix or an endomorphism h of a finite dimensional vector space which does not depend on either the structure theorem for ...
[EN] It is shown in this paper that if X is a class of simple groups such that pi(X) = char X, the X-saturated formation H generated by a finite group cannot be expressed as the Gaschütz product F o G of two non-X-saturated ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Li, Yangming(Springer and Science China Press, 2012-05)
A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series. The structural impact of the partial cover and avoidance ...
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups ...
Esteban Romero, Ramón(Universitat Politècnica de Valencia, 2016-07-24)
[EN] We present some control characters and digits present in the Spanish national identity
document as an example of the application of modular arithmetics to the design of error
correcting codes. This activity has ...
Costa Segarra, Esther Claudia(Universitat Politècnica de València, 2012-12-20)
La finalidad de este proyecto es la creación de una base de datos de problemas
generados con LATEX utilizando software libre, que nos permita generar
listados de problemas ya sean elegido o aleatorios, y poder modificar ...
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite.
One of the most fruitful lines in the ...
Ballester Bolinches, Adolfo; Cosme-Llópez, E.; Esteban Romero, Ramón; Rutten, J.J.M.M.(Alexandru Ioan Cuza University of Iasi, 2015)
The main goal in this paper is to use a dual equivalence in automata theory started in [25] and developed in [3] to prove a general version of the Eilenberg-type theorem presented in [4]. Our principal results confirm the ...
Ballester-Bolinches, A.; Cossey, John; Esteban Romero, Ramón(Universita del Salento, 2013)
[EN] There are different ways to associate to a finite group a certain graph. An interesting question is to analyse the relations between the structure of the group, given in group-theoretical terms, and the structure of ...
A classical result of Gaschütz affirms that given a finite A-generated group G and a prime p, there exists a group G# and an epimorphism phi: G# ---> G whose kernel is an elementary abelian p-group which is universal among ...
Esteban Romero, Ramón(Universidad Politécnica de Madrid, 2013-10-01)
[ES] En este artículo mostramos cómo podemos utilizar el cubo de Rubik para presentar algunos conceptos básicos de la teoría de grupos y cómo podemos usar esta para resolver el cubo de Rubik.
[EN] Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang¿Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in ...
A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite ...