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Listar por autor "Felipe Román, María José"

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An Arad and Fisman's theorem on products of conjugacy classes revisited

Beltrán Felip, Antonio; Felipe Román, María José; Melchor, Carmen (Springer-Verlag, 2022-12)

[EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian ...
Análisis de estructuras algebraicas mediante la modelización de puzzles y rompecabezas

Felipe Román, María José; Sotomayor, Víctor (Editorial Universitat Politècnica de València, 2018-09-26)

[EN] The subject Algebraic Methods and their Applications of the Master in Mathematical Research is focused on showing the applicability that some abstract algebraic structures have in various scientific areas, in both ...
ÁLGEBRA LINEAL

Marín Molina, Josefa; Balaguer Beser, Ángel Antonio; Felipe Román, María José; Capilla Romá, Maria Teresa (Editorial Universitat Politècnica de València, 2012-10-18)

Este libro proporciona un marco general para cualquiera que desee introducirse en el estudio del Álgebra lineal. El principal objetivo del texto es presentar de forma sencilla y práctica un material con definiciones, ...
Clases de conjugación y grupos factorizados

Ortiz Sotomayor, Víctor Manuel (Universitat Politècnica de València, 2016-07-20)

[EN] The purpose of this work is to analyze results on the overall structure of a factorised group from certain information about the sizes of the conjugacy classes of some elements of its factors.
Class sizes of prime-power order p'-elements and normal subgroups

Beltrán, Antonio; Felipe Román, María Josefa; Shao, Changguo (Springer Verlag (Germany), 2015-10)

We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup ...
Conjugacy classes and factorised groups

Ortiz Sotomayor, Víctor Manuel (Universitat Politècnica de València, 2019-09-02)

[ES] Un problema clásico en la teoría de grupos finitos es el estudio de cómo los tamaños de las clases de conjugación influyen sobre la estructura del grupo. En las últimas décadas, numerosos investigadores han obtenido ...
Conjugacy classes contained in normal subgroups: an overview

Beltrán, Antonio; Felipe, María José; Melchor, Carmen (University of Isfahan, 2018)

[EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework ...
Corrigendum on the solvability of groups with four class sizes

Beltrán, Antonio; Felipe Román, María Josefa; SHAO, CHANG GUO (World Scientific Publishing, 2012-12)

The authors have realized that in the proof of Theorem 6 of [1] there is a mistake although the conclusion of the theorem is correct. The proof of the theorem is divided into two cases: when there exist no p-elements of ...
Corrigendum: Some class sizes conditions implying solvability of finite groups

Beltrán Felip, Antonio; Felipe Román, María Josefa (De Gruyter, 2011-01)

[EN] The authors have realized that the proof of Step 1 in [1, Theorem A] is incomplete. Precisely, in the proof of Step 1 we suppose that there exists a p-element x of index m where p is the set of primes dividing m and ...
Cosets of normal subgroups and powers of conjugacy classes

Beltrán, Antonio; Felipe Román, María Josefa (John Wiley & Sons, 2021-09)

[EN] Let G be a finite group and let K=xG be the conjugacy class of an element x of G. In this paper, it is proved that if N is a normal subgroup of G such that the coset xN is the union of K and K-1 (the conjugacy class ...
Estructura de grupos finitos y propiedades aritméticas de los tamaños de clase de conjugación

Alemany Martínez, Elena (Universitat Politècnica de València, 2011-10-24)

La presente memoria se desarrolla en el marco de la Teoría de Grupos Finitos y estudia la relación existente entre la estructura de un grupo y los tamaños de clases de conjugación de sus elementos. En el primer capítulo ...
Finite groups with four conjugacy class sizes

Beltrán, Antonio; Felipe Román, María Josefa (Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2011-03-18)

We determine the structure of all finite groups with four class sizes when two of them are coprime numbers larger than 1. We prove that such groups are solvable and that the set of class sizes is exactly {1, m, n, mk}, ...
Graphs associated to conjugacy classes of normal subgroups in finite groups

Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen (Elsevier, 2015-12-01)

Let G be a finite group and let N be a normal subgroup of G. We attach to N two graphs ΓG(N) and Γ∗ G(N) related to the conjugacy classes of G contained in N and to the set of primes dividing the sizes of these classes, ...
Itô's theorem on groups with two class sizes revisited

Alemany Martínez, Elena; Beltrán, Antonio; Felipe Román, María Josefa (Cambridge University Press, 2012)

Let G be a finite p-solvable group. We prove that if G has exactly two conjugacy class sizes of p'-elements of prime power order, say 1 and m, then m = p(a)q(b), for two distinct primes p and q, and G either has an abelian ...
Jugando con la Teoría de Grupos: rompecabezas, puzzles y otros entretenimientos matemáticos

Felipe, María José; Sotomayor, Víctor (Universitat Politècnica de València, 2018-07-31)

[EN] In this paper we show how to model and to analyse the solubility of some puzzles, brainteasers and other mathematical toys. We make use of basic group theory concepts and the computational algebraic system GAP(Groups, ...
MÉTODOS MATEMÁTICOS

Balaguer Beser, Ángel Antonio; Capilla Romá, Maria Teresa; Felipe Román, María José; Marín Molina, Josefa; Monreal Mengual, Llúcia (Editorial Universitat Politècnica de València, 2014-03-25)

La materia de Métodos Matemáticos tiene un carácter de formación básica necesaria en la mayoría de los primeros cursos de ingeniería. En este texto aparecen temas correspondientes a tres partes del conocimiento matemático ...
Multiplying a conjugacy class by its inverse in a finite group

Beltrán, Antonio; Felipe Román, María José; Melchor, Carmen (Springer-Verlag, 2018-08)

[EN] Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK (-1) = 1 a D a D (-1) with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical ...
Nilpotent and abelian Hall subgroups in finite groups

Beltran, Antonio; Felipe Román, María Josefa; Malle, Gunter; Moreto Quintana, Alexander; Navarro Ortega, Gabriel; Sanus Vitoria, Lucia; Solomon, Ronald; Tiep, Pham Huu (American Mathematical Society, 2016-04)

[EN] We give a characterization of the finite groups having nilpotent or abelian Hall pi-subgroups that can easily be verified using the character table.
Normal sections, class sizes and solvability of finite groups

Akhlaghi, Zeinab; Beltrán Felip, Antonio; Felipe Román, María Josefa (Elsevier, 2014-02-01)

If G is a finite group, we show that any normal subgroup of G which has exactly three G-conjugacy class sizes is solvable. Thus, we give an extension for normal subgroups of the classical N. Itô’s theorem which asserts ...
Normal subgroups and p-regular G-class sizes

Akhlaghi, Zeinab; Beltrán Felip, Antonio; Felipe Román, María Josefa; Khatami, Maryam (Elsevier, 2011-06-15)

Let G be a finite p-solvable group and N be a normal subgroup of G. Suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. In this paper it is shown that, if H is a p-complement of N, then either ...