Felipe Román, María Josefa; Kazarin, Lev S.; Martínez-Pastor, Ana; Sotomayor, Víctor(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; 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 ...