## Mitsugu Hirasaka, Finding n such that every transitive permutation group of degree n is multiplicity-free

Finding n such that every transitive permutation group of degree n is multiplicity-free
Mitsugu Hirasaka
Department of Mathematics, Pusan National University, Pusan, Korea
2009/5/1 Friday 4PM-5PM
This is a joint work with Cai-Heng Li. Let $$\mathcal{MF}$$ denote the set of positive integers n such that each transitive action of degree n is multiplicity-free, and $$\mathcal{PQ}$$ denote the set of $$n\in \mathbb{N}$$ such that n=pq for some primes p, q with $$p[latex]\{pq\in \mathcal{PQ}\mid (p,q-2)=p, q\mbox{ is a Fermat prime}\}$$ and
$$\{pq\in \mathcal{PQ}\mid q=2p-1\}$$
where its proof owes much to classification of finite simple groups.

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