..
Prime Power Or Product Of Two Odd Primes
Table of contents
Prime power degrees
In [1], it was shown that transitive groups of prime power degrees have intersection density equal to \(1\). The proof is by induction on the degree of the group, by quotienting and using the fact that the center of a \(p\)-group is never trivial.
Product of two odd primes
It was shown in [2] that if \(G\) is a transitive group of degree \(pq\), where \(p\) and \(q\) are distinct odd primes, then the intersection density is equal to \(1\), unless \(G\) is quasiprimitive or there is a certain cyclic code of \(\mathbb{F}_q^p\) whose Hamming weight is at most \(p-1\).