Classification of Sylow classes of parabolic and reflection subgroups in unitary reflection groups
- Publisher:
- TAYLOR & FRANCIS INC
- Publication Type:
- Journal Article
- Citation:
- Communications in Algebra, 2020, 48, (9), pp. 3989-4001
- Issue Date:
- 2020-09-01
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| Filename | Description | Size | |||
|---|---|---|---|---|---|
| Classification of Sylow classes of parabolic and reflection subgroups in unitary reflection groups.pdf | Published version | 1.41 MB |
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Let (Formula presented.) be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to inclusion, subject to containing an (Formula presented.) -Sylow subgroup. The classification assists in describing the (Formula presented.) -Sylow subgroups of unitary reflection groups up to group isomorphism. This classification also relates to the modular representation theory of finite groups of Lie type. We observe that unless a parabolic subgroup minimally containing an (Formula presented.) -Sylow subgroup is G itself, the reflection subgroup within the parabolic minimally containing an (Formula presented.) -Sylow subgroup is the whole parabolic subgroup.
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