Constructibly critical subgroup
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
Let be a group of prime power order.
A subgroup of is termed a constructibly critical subgroup if it satisfies the following two conditions:
- The center of , say , is maximal among Abelian characteristic subgroups
- is the intersection of and the inverse image in of the subgroup of
Relation with other properties
Group properties satisfied
A group of prime power order can be realized as a constructibly critical subgroup if it satisfies the following two conditions:
- It is a Frattini-in-center group: Its Frattini subgroup is contained in its center.
- It is a group in which every Abelian characteristic subgroup is central.
Further, any such group is the unique constructibly critical subgroup of itself.