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An Erdős-Ko-Rado theorem for the derangement graph of PGL(\(2,q\)) acting on the projective line. (English) Zbl 1227.05163
Summary: Let \(G= \text{PGL}(2, q)\) be the projective general linear group acting on the projective line \(\mathbb{P}_q\). A subset \(S\) of \(G\) is intersecting if for any pair of permutations \(\pi\), \(\sigma\) in \(S\), there is a projective point \(p\in\mathbb{P}_q\) such that \(p^\pi= p^\sigma\). We prove that if \(S\) is intersecting, then \(|S|\leq q(q- 1)\). Also, we prove that the only sets \(S\) that meet this bound are the cosets of the stabilizer of a point of \(\mathbb{P}_q\).

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05D05 Extremal set theory
05E10 Combinatorial aspects of representation theory
Software:
GAP
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