| Speaker: Luke Morgan Affiliation: The University of Western Australia Time: 14:00 Tuesday, 27 June, 2017 Location: 303-G15 |
| A transitive permutation group is called semiprimitive if each normal subgroup is transitive or semiregular. The class of semiprimitive groups includes all primitive, quasiprimitive, innately transitive and Frobenius groups. Apart from being a generalisation of these important classes of permutation groups, motivation to study this class came from problems in abstract algebra and in algebraic graph theory. Further, solutions to these problems has been stymied by the lack of any apparent structure in such groups and the prevalence of wild examples. In this talk I will report on joint work with Michael Giudici in which we brought some clarity to this issue. We found that there is indeed structure to a semiprimitive group, although not as precise as that given by the seminal O'Nan-Scott Theorem for primitive groups. We also exhibit enough rough structure to explain how semiprimitive groups are built from innately transitive groups. Along the way I'll mention plenty of examples, some recent results on statistical questions about this class and time permitting some application of this theory to the motivating problems. |