Sylow normalizer

The article defines a subgroup property, where the definition may be in terms of a particular prime number that serves as parameter
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Definition

Symbol-free definition

A subgroup of a finite group is said to be a Sylow normalizer if it occurs as the normalizer of a Sylow subgroup.

Relation with other properties

Weaker properties

• Abnormal subgroup
• Local subgroup for a prime
• Local subgroup

Facts

Since all the $p$-Sylow subgroups are conjugate, all the normalizers of $p$-Sylow subgroups are conjugate.