Group in which the ZJ-functor controls fusion for a prime

From Groupprops
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

Suppose G is a finite group and p is a prime number. We say that G is a group in which the ZJ-functor controls fusion for p if the ZJ-functor, viewed as a conjugacy functor on G, controls fusion in G with respect to p. In other words, given a p-Sylow subgroup P of G and two subsets A,B of P that are conjugate in G, the subsets A,B are conjugate in N_G(Z(J(P)).

Relation with other properties

Stronger properties