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arXiv Open Access 2025

On the number and sizes of double cosets of Sylow subgroups of the symmetric group

Persi Diaconis Eugenio Giannelli Robert M. Guralnick Stacey Law Gabriel Navarro +2 lainnya
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Abstrak

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.

Topik & Kata Kunci

math.GR

Penulis (7)

P

Persi Diaconis

E

Eugenio Giannelli

R

Robert M. Guralnick

S

Stacey Law

G

Gabriel Navarro

B

Benjamin Sambale

H

Hunter Spink

Format Sitasi

APA MLA BibTeX
Diaconis, P., Giannelli, E., Guralnick, R.M., Law, S., Navarro, G., Sambale, B. et al. (2025). On the number and sizes of double cosets of Sylow subgroups of the symmetric group. https://arxiv.org/abs/2504.01149

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Tahun Terbit
2025
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en
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arXiv
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Open Access ✓