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

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...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series A 2018-07, Vol.157, p.461-499
Main Authors: Long, Ling, Plaza, Rafael, Sin, Peter, Xiang, Qing
Format: Article
Language:English
Subjects:
Character table
Erdős–Ko–Rado theorem
Hypergeometric function over finite field
Intersecting family
Legendre sum
Soto-Andrade sum
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Summary: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.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2018.03.006