This talk will be on zoom only with zoom meeting ID 986 2892 7517

I will start with dihedral groups as a motivating example to talk about indices of non-transitive subgroups. Then we will shift back to the general case - the discussion boils down to a fascinating property of subgroups of permutation groups of prime degree.

From there, we will discuss a theorem of Burnside that states that a group G which is at least doubly transitive must either be simple or must contain a simple group H as a normal subgroup.

Finally, we will talk about the history of the Classification of the finite simple groups and give Guralnick’s result about the four cases of subgroups of almost simple transitive permutation groups of prime degree p.