I have to prove that a transitive permutation group, $G$, is regular. What is the definition of regular?
In addition, my lecturer hinted that a transitive permutation group is regular if and only if there is no corefree proper subgroup. My understanding is that the normal core of $H$ in $G$, with $H<G$, is the intersection of all the conjugates of $H$ (which is equivalent to several other definitions, http://groupprops.subwiki.org/wiki/Normal_core ). From this, I've inferred that he means that for every subgroup, $H<G$, the core of $H$ in $G$ is the trivial group. Is this the correct definition?