Group in which every p-local subgroup is of Glauberman type
The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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Let be a finite group and be a prime number. We say that every p-local subgroup is of Glauberman type if every p-local subgroup (i.e., the normalizer of a non-identity -subgroup) is a group of Glauberman type for the prime .
Relation with other properties
- Group in which the ZJ-functor controls fusion: The proof follows by combining the fact that control of fusion is local and the fact that Glauberman type implies ZJ-functor controls fusion, which in turns follows from the fact that conjugacy functor whose normalizer generates whole group with p'-core controls fusion