Beltran, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Cambridge University Press (CUP), 2016-10)
Let G be a finite group and let N be a normal subgroup of G. We determine the structure of N when the diameter of the graph associated to the G-conjugacy classes contained in N is as large as possible, that is, equal to three.
Felipe Román, María Josefa; Monserrat Delpalillo, Francisco José; Sotomayor, Víctor(Facultad de Ciencias. Departamento de Matemáticas Fundamentales. UNED, 2019)
[ES] Los rápidos avances científico-tecnológicos determinan un constante y raudo cambio tanto en la vida cotidiana como en la percepción del mundo que nos rodea, lo cual implica una necesidad de adaptación del conocimiento ...
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 ...
Beltrán, Antonio; Felipe Román, María Josefa(World Scientific Publishing, 2012-04)
It is shown that if the set of conjugacy class sizes of a finite group G is {1,m,n,mn}, where m, n are positive integers which do not divide each other, then G is up to central factors a {p,q}-group. In particular, G is solvable.
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; Felipe Román, María Josefa; Shao, Changguo(De Gruyter, 2015-01)
. Let N be a normal subgroup of a group G and let p be a prime. We prove that if
the p-part of jx
Gj is a constant for every prime-power order element x 2 N n Z.N /, then
N is solvable and has normal p-complement.
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 ...
Alemany Martínez, Elena(Universitat Politècnica de València, 2011-12-30)
Estudio sobre la influencia de los tamaños de clases de conjugación de todos o parte de los elementos de un grupo en la estructura del mismo. En particular, se estudia la estructura de un grupo con dos tamaños de clases ...
Beltrán, Antonio; Felipe Román, María Josefa(Springer Verlag (Germany), 2014-12)
Given a finite group G which possesses a non-abelian simple normal subgroup N having exactly four G-class sizes, we prove that N is isomorphic to PSL(2,2a) with a≥2. Thus, we obtain an extension for normal subgroups of the ...
Beltrán, Antonio; Felipe Román, María Josefa(Debreceni egyetem matematika intézet, 2013)
[EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa
}, with p a prime not dividing m, then N ...
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 ...
Akhlaghi, Z.; Beltrán, Antonio; Felipe Román, María Josefa; Khatami, M.(Springer Verlag (Germany), 2012-07)
Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m < n and m does not divide n. In this paper, we show that N is solvable, and we determine ...
Beltrán, Antonio; Felipe Román, María Josefa(Springer Verlag (Germany), 2013-08)
Let G be a finite p-solvable group for some prime p and suppose that the set of p-regular conjugacy class sizes is {1,m,mn} with (m,n)=1 and m coprime to p. We show that m=qb for some prime q and we describe the structure ...
Akhlaghi, Z.; Beltran, A.; Felipe Román, María Josefa(De Gruyter, 2013-07)
Let G be a finite group and N be a normal subgroup of G and suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. It is shown that N is solvable and that if H is a p-complement of N, then either ...
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 ...