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 ...
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) ...
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 ...