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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
##### Keywords:
derangement graph; independent sets; Erdős-Ko-Rado theorem
GAP
Full Text:
##### References:
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