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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 $G\left(m,p,n\right)$ is a coset of the stabilizer of a point in $\left\{1,\cdots ,n\right\}$ provided $n$ is sufficiently large.
##### MSC:
 05E10 Combinatorial aspects of representation theory 20C15 Ordinary representations and characters of groups 05D05 Extremal set theory
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