Kazarin, L. S.; Martínez Pastor, Ana; Perez Ramos, Maria Dolores(Elsevier, 2013-04-01)
[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime ...
Arroyo Jordá, Milagros; Arroyo Jordá, Paz; Dark, Rex; Feldman, Arnold D.; Pérez-Ramos, María Dolores(Springer-Verlag, 2022)
[EN] Classical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent subgroups, coincide with nilpotent projectors and with nilpotent covering subgroups, and they ...
Arroyo Jordá, Milagros; Arroyo Jordá, Paz; Dark, R.; Feldman, A. D.; Pérez Ramos, M. D.(Springer-Verlag, 2022-08)
[EN] Let pi be a set of primes. We show that pi-separable groups have a conjugacy class of F-injectors for suitable Fitting classes F, which coincide with the usual ones when specializing to soluble groups.
Two subgroups and of a group are said to be totally completely conditionally permutable (tcc-permutable) if permutes with for some , for all and all . In this paper, we study finite products of tcc-permutable subgroups, ...
[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 ...
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) ...
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 ...
[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 ...
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
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 ...