## Erdős-Ko-Rado theorem for irreducible imprimitive reflection groups.(English)Zbl 1250.05118

Summary: Let $$\Omega$$ be a finite set, and let $$G$$ be a permutation group on $$\Omega$$. A subset $$H$$ of $$G$$ is called intersecting if any $$\sigma, \pi \in H$$ have at least one point. We show that a maximal intersecting subset of an irreducible imprimitive reflection group $$G(m, p, n)$$ is a coset of the stabilizer of a point in $$\{1, \dots, n\}$$ provided $$n$$ is sufficiently large.

### MSC:

 05E10 Combinatorial aspects of representation theory 20C15 Ordinary representations and characters 05D05 Extremal set theory
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### References:

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