Title

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

Document Type

Article

Publication Date

7-1-2018

Abstract

We consider the action of the 2-dimensional projective special linear group PSL(2,q) on the projective line PG(1,q) over the finite field Fq, where q is an odd prime power. A subset S of PSL(2,q) is said to be an intersecting family if for any g1,g2∈S, there exists an element x∈PG(1,q) such that xg1=xg2. It is known that the maximum size of an intersecting family in PSL(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.

Publication Source (Journal or Book title)

Journal of Combinatorial Theory. Series A

First Page

461

Last Page

499

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