Strongly contranormal subgroup
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]
This is an opposite of normality
Definition with symbols
Relation with other properties
Related group properties
A group that possesses a strongly contranormal subgroup is termed a quasiprimitive group.
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
Any strongly contranormal subgroup of a strongly contranormal subgroup is strongly contranormal. This follows directly from the definition.
The whole group is strongly contranormal as a subgroup of itself. In contrast, the trivial subgroup is strongly contranormal only if the group is trivial.