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 ...
[EN] Two subgroups A and B of a finite group G are said to be tcc-permutable if X permutes with Y for some g epsilon (X, Y), for all X <= A and all Y <= B. Some aspects about the normal structure of a product of two ...
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, ...
Two subgroups A and B of a group G are said to be totally completely conditionally permutable (tcc-permutable) in G if X permutes with Yg for some g ¿ ¿X, Y¿ for all X ¿ A and Y ¿ B. We study the belonging of a finite ...
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 ...
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 ...
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 ...
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 ...