Type: Seminar

Distribution: World

Expiry: 25 Jan 2007

Auth: billu@galois.maths.usyd.edu.au

Speaker: Peter Brooksbank (Bucknell) Title: Constructive recognition of simple groups Time & Place: 2-3pm, Thursday 25 January, Carslaw 535 Abstract: Given a finite group $G$, known to be isomorphic to a simple group $H$ (we regard $H$ is the {\em standard copy} of the simple group), we consider the algorithmic problem of writing down an explicit isomorphism from $H$ to $G$. This problem, known as the {\em constructive recognition problem}, has important applications to several other algorithmic problems of current interest. Among these are the problem of constructing a composition series for a finite matrix group, and constructing the maximal subgroups of a permutation group. In this talk I will give a more precise definition of a constructive recognition algorithm and indicate how such algorithms are applied to the problems mentioned above. I will also outline some of the algorithmic difficulties one is confronted with when devising such algorithms.