Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Diaconis, Persi, Giannelli, Eugenio, Guralnick, Robert M., Law, Stacey, Navarro, Gabriel, Sambale, Benjamin, Spink, Hunter
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979286293
Cites:
Cited by:
Related to: