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On the number and sizes of double cosets of Sylow subgroups of the symmetric group
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On the number and sizes of double cosets of Sylow subgroups of the symmetric group
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Let $P_n$ be a Sylow $p$-subgroup of the symmetric group $S_n$. We investigate the number and sizes of the $P_n\setminus S_n\ /\ P_n$ double cosets, showing that most double cosets have maximal size when $p$ is odd, or equivalently, that $P_n\cap P_n^x=1$ for most $x\in S_n$ when $n$ is large. We also find that all possible sizes of such double cosets occur, modulo a list of small exceptions.
Forward citations
Cited by 2 Pith papers
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On the sizes of the maximal prime powers divisors of factorials
For any prime p there exists n0(p) such that p to the power of its factorial valuation exceeds that of every larger prime q for all n at or above n0, and for twin primes the smallest such n0 is exactly p(p+1)/2.
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