Abstract Let 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 -Sylow subgroup. The classification assists in describing the -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 -Sylow subgroup is G itself, the reflection subgroup within the parabolic minimally containing an -Sylow subgroup is the whole parabolic subgroup.

中文翻译：

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酉反射群中抛物线和反射子群的 Sylow 类的分类

摘要 设 为有限酉反射群阶的素数除数。我们将在包含方面最小的抛物线和反射子群进行共轭分类，但要包含一个 -Sylow 子群。该分类有助于描述幺正反射群的 -Sylow 子群直到群同构。这种分类也与李型有限群的模表示理论有关。我们观察到，除非最低限度包含 -Sylow 子群的抛物线子群是 G 本身，否则最低限度包含 -Sylow 子群的抛物线子群内的反射子群就是整个抛物线子群。