Computing with maximal subgroups
Colva Roney-Dougal
St Andrews
This talk will describe techniques for computing the
maximal subgroups of finite permutation groups. Apart from being
interesting in themselves, the maximal subgroups of a group have many
applications: for instance one may use them to investigate the full
subgroup lattice, or to investigate combinatorial and geometric
structures on which the group acts as automorphisms.
We will begin with a brief survey of existing algorithms, before
discussing recent work of Derek Holt and myself which uses the
geometries preserved by the finite classical groups to construct
their maximal subgroups in Magma.