Seminario: Finite primitive groups as products of point stabilizers

Venerdì 11 Dicembre 2015, ore 11:30 - Aula 2AB40 - Martino Garonzi



Venerdì 11 Dicembre 2015 alle ore 11:30 in Aula 2AB40, Martino Garonzi (Università di Brasilia) terrà un seminario dal titolo "Finite primitive groups as products of point stabilizers".

I will present a recent work joint with Attila Maróti, Iulian Simion and Dan Levy about factorizations of finite primitive groups using point stabilizers. A primitive group can be defined as a group G that possesses a maximal subgroup M such that the intersection of the conjugates of M is trivial. M is then a point stabilizer of the transitive action of right multiplication of G on the set of the right cosets of M, and by transitivity every point stabilizer of this action is conjugated to M. Let G be a finite primitive group and let n denote the index of M in G. Employing the O'Nan-Scott theorem, that is an important classification theorem of primitive groups, we showed that if M is nontrivial then G is the product of at most c*log(n) conjugates of M, where c is a universal constant.