BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]
Relation with other properties
|property||quick description||proof of implication||proof of strictness (reverse implication failure)||intermediate notions|
|Verbal subgroup|||FULL LIST, MORE INFO|
|1-endomorphism-invariant subgroup|||FULL LIST, MORE INFO|
|Fully invariant subgroup|||FULL LIST, MORE INFO|
|1-automorphism-invariant subgroup|||FULL LIST, MORE INFO|
|Quasiautomorphism-invariant subgroup|||FULL LIST, MORE INFO|
|Characteristic subgroup|||FULL LIST, MORE INFO|
|Normal subgroup||Potentially power subgroup|FULL LIST, MORE INFO|
This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup 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