Seminario: Minimally transitive groups and a conjecture of Pyber

Venerdì 30 Ottobre 2015, ore 11:30 - Sala Riunioni VII Piano - Gareth Tracey



Venerdì 30 Ottobre 2015 alle ore 11:30 in Sala Riunioni VII Piano, Gareth Tracey (Università di Warwick) terrà un seminario dal titolo "Minimally transitive groups and a conjecture of Pyber".

Suppose that G is a transitive permutation group, of degree n, but that G needs a large number of generators (in terms of n). If possible, we would like to "reduce" the number of generators, whilst keeping our group transitive. More precisely, we would like to take a subset X of G, minimal with the property that is transitive. The question is: can we find a good upper bound for |X|, in terms of n? In this talk, we discuss the history of this question,
including an old conjecture of Pyber, and some new results.