# Peter J. Cameron:The geometry of diagonal groups

**Time: **
Wed 2021-09-22 10.15 - 11.15

**Location: **
Zoom meeting ID: 654 5562 3260

**Participating: **
Peter J. Cameron (University of St Andrews)

Abstract: Diagonal groups arise in the celebrated O'Nan--Scott Theorem on finite primitive permutation groups, but in fact they can be defined for any dimension and any group, finite or infinite. They turn out to be automorphism groups of join-semilattices of the partition lattice on a set. The two-dimensional case corresponds precisely to Latin squares, but in higher dimensions a group emerges naturally. (This is similar to the situation in projective geometry where there are many projective planes, but higher-dimensional spaces are coordinatised by division rings.) They also give rise to a family of graphs including Latin square graphs and folded cubes. Work is in progress on extending the notion of mutually orthogonal Latin squares to this higher-dimensional situation.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260