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 ...
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.
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 ...
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 ...
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 ...
[EN] Let G be a finite group, and let Delta(G) be the prime graph built on its set of conjugacy class sizes: this is the (simple undirected) graph whose vertices are the prime numbers dividing some conjugacy class size of ...
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, ...
Artidiello Moreno, Santiago de Jesús; Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Taylor & Francis Ltd, 2013-10)
In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King s family of fourth-order schemes is obtained as an special case. We also present results ...
Felipe Román, María Josefa; Kazarin, Lev S.; Martínez-Pastor, Ana; Sotomayor, Víctor(Springer-Verlag, 2020-12)
[EN] Let the group G = AB be the product of subgroupsAandB, and letpbe a prime. We prove thatpdoes not divide the conjugacy class size (index) of eachp-regular element of prime power order x is an element of A boolean OR ...
Felipe Román, María Josefa; Grittini, N.; Sotomayor, Víctor(Springer-Verlag, 2020-10)
[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. ...
Beltrán, Antonio; Camina, Rachel Deborah; Felipe Román, María Josefa; Melchor, Carmen(Springer-Verlag, 2020-04)
[EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability ...
Felipe Román, María Josefa; Martínez-Pastor, Ana; Sotomayor, Víctor(Springer-Verlag, 2017)
[EN] Let the group G = AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A. B have prime power indices in G, for some prime p. More generally, we also consider ...
Felipe Román, María José; Martínez-Pastor, Ana; Sotomayor, Víctor(Springer-Verlag, 2020-02)
[EN] We provide structural criteria for some finite factorised groups G = AB when the conjugacy class sizes in G of certain pi-elements in A boolean OR B are either pi-numbers or pi'-numbers, for a set of primes pi. In ...
Beltran, Antonio; Felipe Román, María Josefa; Melchor, Carmen(University of Isfahan, 2020-03)
[EN] We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect ...
Felipe, María José; Martínez Pastor, Ana; Sotomayor, Víctor(Elsevier, 2017)
[EN] We obtain some structural properties of a factorised group G = AB, given that the conjugacy class sizes of certain elements in A boolean OR B are not divisible by p(2), for some prime p. The case when G = AB is a ...
Beltrán, A.; Felipe Román, María Josefa; Melchor, C.(Springer-Verlag, 2018)
[EN] We prove that if a finite group G contains a conjugacy class K whose square is of the form 1¿D, where D is a conjugacy class of G, then ¿K¿ is a solvable proper normal subgroup of G and we completely determine its ...
Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Springer-Verlag, 2017-01)
[EN] Let G be a finite group and N a normal subgroup of G. We determine the
structure of N when the graph G(N), which is the graph associated to the conjugacy
classes of G contained in N, has no triangles and when the graph ...
Sotomayor, Víctor; Felipe Román, María Josefa; Martínez-Pastor, Ana(Springer-Verlag, 2019-02)
[EN] An element g of a finite group G is said to be vanishing inG if there exists an irreducible character of G such that (g)=0; in this case, g is also called a zero of G. The aim of this paper is to obtain structural ...