Weakly closed conjugacy functor

From Groupprops
Revision as of 21:47, 2 March 2009 by Vipul (talk | contribs) (New page: {{conjugacy functor property}} ==Definition== Suppose <math>G</math> is a finite group, <math>p</math> a prime number, and <math>W</math> a [[defining ingredient::conjugacy funct...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article defines a property that can be evaluated for a conjugacy functor on a finite group. |View all such properties

Definition

Suppose G is a finite group, p a prime number, and W a conjugacy functor on G with respect to p. We say that W is weakly closed in G with respect to p if W(P) is a weakly closed subgroup of P.

For instance, a p-normal group is a group in which the conjugacy functor that arises by taking the center is weakly closed.