"Covering a group by conjugates of a coset".

Abstract:

For every doubly transitive permutation group G the conjugates
of a non-trivial coset of a point stabilizer H cover the group.
This implies that every non-trivial conjugacy class of elements
of G that contains an element of H does contain a transversal
of H in G and that every other non-trivial conjugacy class
contains a transversal for the set of cosets of H in G different
from H.

We study the finite groups satisfying this property; more precisely
the class of primitive permutation groups, called
CCI groups, that in fact properly contains the class of 2-transitive
permutation groups