This article defines a particular kind of map (functor) from a set of subgroups of a group to a set (possibly the same set) of subgroups
This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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Origin of the term
The term was first used in the paper Transfer and fusion in finite groups by Finkel and Gorenstein in the Journal of Algebra, 6 (1967), Pages 242-255.
Definition with symbols
Let be a group and a prime. A central functor is a map from the collection of -subgroups of to the collection of -subgroups of that satisfies:
- For any -subgroup , .
- For any -subgroup , and any , .
- If then .
Clearly, every central functor is a conjugacy functor.
Examples of central functor include the center and the powers of elements in the center.