# Category:Group properties obtained via the subgroup property collapse operator

From Groupprops

This category lists group properties obtained by collapsing two subgroup properties. In other words, a group has the given group property if every subgroup satisfying one subgroup property also satisfies the second subgroup property.

## Pages in category "Group properties obtained via the subgroup property collapse operator"

The following 22 pages are in this category, out of 22 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### G

- Gaschütz group
- Group in which every automorph-conjugate subgroup is characteristic
- Group in which every characteristic subgroup is fully invariant
- Group in which every characteristic subgroup is strictly characteristic
- Group in which every cyclic subgroup is 2-subnormal
- Group in which every finite abelian subgroup is cyclic
- Group in which every finite subgroup is cyclic
- Group in which every fully invariant subgroup is verbal
- Group in which every normal subgroup is a central factor
- Group in which every normal subgroup is a direct factor
- Group in which every normal subgroup is characteristic
- Group in which every normal subgroup is fully invariant
- Group in which every permutable subgroup is normal
- Group in which every pronormal subgroup is normal
- Group in which every retract is a direct factor
- Group in which every retract is regular
- Group in which every subgroup is automorph-conjugate
- Group in which every subnormal subgroup is 2-subnormal
- Group in which every weakly abnormal subgroup is abnormal