The geometry of diagonal groups

Peter Cameron (University of St. Andrews)

Wednesday 28th October, 2020 16:00-17:00 online (zoom)


Diagonal groups form one of the classes of groups in the celebrated O'Nan--Scott theorem which underpins the application of finite simple groups to permutation group theory. But they form a much wider class. A diagonal group is built from a dimension and an arbitrary group, not necessarily simple or even finite. We construct and characterise a geometric object whose automorphism group is the diagonal group if the dimension is at least 3. In dimension 2 these objects are equivalent to Latin squares and exist in great profusion, but in higher dimension the group emerges naturally from the combinatorial axioms. The work links group theory, combinatorics and statistics.

(joint work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider)


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