Two subgroups X and Y of a group G are said to be conditionally permutable in G if X permutes with Y(g) for some element g E G. i.e., XY(g) is a subgroup of G. Using this permutability property new criteria for the product ...
Felipe Román, María Josefa; Kazarin, Lev S.; Martínez-Pastor, Ana; Ortiz-Sotomayor, Víctor Manuel(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 ...
Kazarin, L. S.; Martínez Pastor, Ana; Perez Ramos, Maria Dolores(European Mathematical Society-Publishing House, 2015)
[EN] The aim of this paper is to prove the following result: let π be a set of odd primes. If the finite group G = AB is a product of two π-decomposable subgroups A = Oπ(A)×Oπ (A) and B = Oπ(B)×Oπ (B), then Oπ(A)Oπ(B)=Oπ(B)Oπ(A) ...
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.; Ortiz-Sotomayor, Víctor Manuel(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 ...
We continue here our study of pairwise mutually and pairwise totally permutable
products. We are looking for subgroups of the product in which the given factorization
induces a factorization of the subgroup. In the case ...
Felipe Román, María Josefa; Martínez-Pastor, Ana; Ortiz-Sotomayor, Víctor Manuel(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 ...
Ballester-Bolinches, A.; Beidleman, J.C.; Esteban Romero, Ramón(Cambridge University Press (CUP): STM Journals - No Cambridge Open, 2014-06)
All groups are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as its proper subgroup. He, Qiao and Wang [7] proved that ...
Gallego, María Pilar; Hauck, Peter; Kazarin, Lev S.; Martínez-Pastor, Ana; Pérez-Ramos, María Dolores(MDPI AG, 2020-09)
[EN] For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if < a, b > is an element of L for all a is an element of A and b is an element of B. In a previous ...
Felipe Román, María José; Martínez-Pastor, Ana; Ortiz-Sotomayor, Víctor Manuel(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 ...
[EN] We give criteria to characterize abnormal, pronormal and locally pronormal subgroups of a direct product of two finite groups A×B, under hypotheses of solvability for at least one of the factors, either A or B.
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 ...
Felipe, María José; Martínez Pastor, Ana; Ortiz-Sotomayor, Víctor Manuel(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; 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 ...