| Autor: |
TOWNSEND, KANE DOUGLAS |
| Předmět: |
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| Zdroj: |
Bulletin of the Australian Mathematical Society; Feb2018, Vol. 97 Issue 1, p57-68, 12p |
| Abstrakt: |
Let a prime $p$ divide the order of a finite real reflection group. We classify the reflection subgroups up to conjugacy that are minimal with respect to inclusion, subject to containing a $p$-Sylow subgroup. For Weyl groups, this is achieved by an algorithm inspired by the Borel–de Siebenthal algorithm. The cases where there is not a unique conjugacy class of reflection subgroups minimally containing the $p$-Sylow subgroups are the groups of type $F_{4}$ when $p=2$ and $I_{2}(m)$ when $m\geq 6$ is even but not a power of $2$ for each odd prime divisor $p$ of $m$. The classification significantly reduces the cases required to describe the $p$-Sylow subgroups of finite real reflection groups. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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