Description
A map is regular if its automorphism group acts regularly on the flag set of the map. A weaker concept is that of an orientably-regular map (on an orientable surface) in which the group of all orientation-preserving automorphisms acts regularly on the arc set of the map.
We will be interested in regular and orientably-regular maps whose automorphism groups are quasiprimitive when considered as permutation groups on the vertex set; this is equivalent to the condition that no non-trivial normal quotient produces a map with more than one vertex. By Praeger’s generalisation of the O’Nan-Scott Theorem, quasiprimitive permutation groups split naturally into 8 classes. We will investigate the existence of vertex-quasiprimitive regular and orientably-regular maps with automorphism group in a given class.
This is a report on a joint work with Yan Wang and Cai Heng Li.
Primary author
Prof.
Jozef ŠIRÁŇ
(Open University and Slovak University of Technology)
