Ana Martínez Pastor will give the talk «On products of π-decomposable groups and Hall-like theorems» at 2021 Zassenhaus Groups and Friends Conference, online, on 04/06/2021 at 15.15. More information:
Vicent Pérez-Calabuig will give the talk «On the computability of the abelian kernel of an inverse semigroup» at 2021 Zassenhaus Groups and Friends Conference, online, on 28/05/2021 at 15.50. More information:
María Dolores Pérez Ramos will give the talk entitled
Thompson-like characterization of solubility for products of groups
at the 2020 Zassenhaus Groups and Friends Conference online on 29th May 2020 at 15.55. The link for the talk and its recording appear on http://www2.math.binghamton.edu/p/zassenhaus/zassenhaus_2020/home.
A remarkable result of Thompson states that a finite group is soluble if
and only if its two-generated subgroups are soluble. This result has been
sharply generalized, and it is in the core of a wide area of study in the theory
of groups, aiming for global properties of groups from local properties of two-
generated (or more generally, n-generated) subgroups. We report about an
extension of Thompson’s theorem from the perspective of factorized groups.
We prove that for a finite group G = AB, with A, B subgroups of G, if ha, bi
is soluble for all a ∈ A and all b ∈ B, then [A, B] is soluble. In that case, the
group G is said to be an S-connected product of the subgroups A and B, for
the class S of all finite soluble groups. As an application, deep results about
connected products of finite soluble groups, for other relevant classes of
groups, are extended to the finite universe. Collaboration with M. P. Gállego (U.
Zaragoza, Spain), P. Hauck (U. Tübingen, Germany), L. Kazarin (U. Yaroslavl,
Russia), A. Martı́nez-Pastor (U. Politècnica de València, Spain) .