Characteristic p-functor that gives a characteristic subgroup

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This article defines a property that can be evaluated for a characteristic p-functor in the context of a finite group.|View other such properties

Definition

Suppose p is a prime number and G is a finite group such that W is a conjugacy functor for G for the prime p arising from a characteristic p-functor. We say that W is a characteristic p-functor that gives a characteristic subgroup if it satisfies the following equivalent conditions:

  1. For every pair of p-Sylow subgroups P,Q of G, W(P) = W(Q).
  2. For every pair of p-Sylow subgroups P,Q of G, W(P) is a normal subgroup of Q.
  3. Each of these:
  4. Each of these:
  5. Each of these:

Equivalence of definitions

Further information: equivalence of normality and characteristicity conditions for conjugacy functor