Omega-1 of center is normality-large in nilpotent p-group
Let be a nilpotent p-group, i.e., a nilpotent group where the order of every element is a power of the prime . Then, the subgroup is a normality-large subgroup of : its intersection with every nontrivial normal subgroup is nontrivial.
Note that if is a finite p-group, i.e., a group of prime power order, then it is nilpotent.
- Minimal normal implies contained in Omega-1 of center for nilpotent p-group
- Socle equals Omega-1 of center for nilpotent p-group
- Minimal characteristic implies contained in Omega-1 of center for nilpotent p-group