This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
Definition with symbols
Relation with other properties
This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity
We need to show that if with each conjugate-large in the next, is conjugate-large in .
The proof of this is as follows: let such that is trivial. We first show that is trivial by observing that is conjugate-large in . We then show that is trivial using the fact that is conjugate-large in .
Conjugate-largeness is an identity-true subgroup property, but it is not in general trivially true.