Computational Algebra Seminar: Brooksbank -- Constructive recognition of simple groups

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.