Group of prime power order may have multiple characteristic subgroups of prime order
- Maximal among abelian characteristic subgroups may be multiple and isomorphic
- Characteristic maximal not implies isomorph-free in group of prime power order
For , we can take:
Then, has three characteristic subgroups of order two:
- The subgroup is the commutator subgroup.
- The subgroup is the unique subgroup generated by the unique element that is a square but not a commutator.
- The subgroup is the unique subgrou pgenerated by the element that is a producto f squraes but not a square itself.