[EN] The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent ...
[EN] The main result in the paper states the following: Let π be a set of odd primes. Let the finite group G=AB be the product of a π -decomposable subgroup A=Oπ(A)×Oπ′(A) and a π -subgroup B . Then Oπ(A)⩽Oπ(G); ...
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) ...
[EN] Let the group G = AB be a product of two π-decomposable subgroups A = Oπ(A) × Oπ′ (A) and B = Oπ(B) × Oπ′ (B) where π is a set of primes. The authors conjecture that Oπ(A)Oπ(B) = Oπ(B)Oπ(A) if π is a set of odd primes. ...
Let G be a finite group and Gp be a Sylow p-subgroup of G for a prime
p in pi(G), the set of all prime divisors of the order of G. The automiser
Ap(G) is defined to be the group NG(Gp)/GpCG(Gp). We define the
Sylow graph ...
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 ...
Alegre Gil, Maria Carmen; Martínez Pastor, Ana; Pedraza Aguilera, María Carmen(Editorial Universitat Politècnica de València, 1997-07-23)
Se trata de un texto de problemas resueltos en el ámbito de la Matemática Discreta,
destinado principalmente a estudiantes de Informática, aunque muchos de los tópicos
incluidos pueden ser útiles a estudiantes de otras ...
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; 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 ...
[EN] Two subgroups H and K of a finite group G are said to be
N -connected if the subgroup generated by x and y is a nilpotent group,
for every pair of elements x in H and y in K. This paper is devoted to
the study of ...
[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.
Soler Facundo, María(Universitat Politècnica de València, 2015-10-19)
[EN] This survey is a contribution to our understanding of how subgroups with various embedding properties can be detected and characterized in the subgroup lattice of a direct product of two groups
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 ...
Kazarin, L.S.; Martínez-Pastor, Ana; Pérez-Ramos, M. D.(Springer-Verlag, 2020-11-01)
[EN] The aim of this paper is to prove the following result: Let pi be a set of odd primes. If the group G = AB is the product of two p-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then G has a unique ...
Hauck, P.; Kazarin, L. S.; Martínez-Pastor, Ana; Pérez-Ramos, M. D.(Springer-Verlag, 2021-02)
[EN] A remarkable result of Thompson states that a finite group is soluble if and only if all its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area ...
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 ...