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]
Definition with symbols
- (Left-action convention): A subgroup of a group is termed procharacteristic in if, for any automorphism of , there exists such that .
- (Right-action convention): A subgroup of a group is termed procharacteristic in if, for any automorphism of , there exists such that .
Relation with other properties
- Automorph-conjugate subgroup
- Weakly procharacteristic subgroup
- Pronormal subgroup
- Weakly pronormal subgroup
- Any procharacteristic subgroup of a normal subgroup is pronormal. Further information: Procharacteristic of normal implies pronormal
- A subgroup of a group is procharacteristic in if and only if whenever is normal in some group , is pronormal in . Further information: Left residual of pronormal by normal is procharacteristic