paper

Characterization of intersecting families of maximum size in $P S L (2, q)$

arXiv:1608.07304

Abstract

We consider the action of the $2$ -dimensional projective special linear group $P S L (2, q)$ on the projective line $P G (1, q)$ over the finite field $\F_q$, where $q$ is an odd prime power. A subset $S$ of $P S L (2, q)$ is said to be an intersecting family if for any $g_{1}, g_{2} \in S$ , there exists an element $x \in P G (1, q)$ such that $x^{g_{1}} = x^{g_{2}}$ . It is known that the maximum size of an intersecting family in $P S L (2, q)$ is $q (q - 1) /2$ . We prove that all intersecting families of maximum size are cosets of point stabilizers for all odd prime powers $q > 3$ .

32 pages, corrected some minor errors; in particular, stated the new Theorem 1 and 3 with the extra condition that $q > 3$

Characterization of intersecting families of maximum size in PSL(2,q)

Abstract

Characterization of intersecting families of maximum size in $P S L (2, q)$