Seminario: Minimal and invariable generation of permutation and linear groups

Venerdì 23 Ottobre 2015, ore 11:30 - Aula 2AB40 - Gareth Tracey



Venerdì 23 Ottobre 2015 alle ore 11:30 in Aula 2AB40, Gareth Tracey (Università di Warwick) terrà un seminario dal titolo "Minimal and invariable generation of permutation and linear groups".

A subset {x1,x2,...,xt} of a group G is said to invariably generate G if x1^g1,x2^g2,...,xt^gt generates G for every t-tuple (g1, g2,...,gt) in G^t. Motivated by a problem in computational Galois Theory, Chebotarev, and later Dixon, studied invariable generation in the symmetric groups Sn. More recently, people have begun to ask: what happens for general finite groups? In this talk, we study the problem for certain classes of permutation/linear groups G (of degree/dimension n, say),paying particular attention to the following question: if d_I (G) denotes the size of the smallest invariable generating set for G, then what is the best possible upper bound for d_I (G) in terms of n?