Minimal normal implies contained in Omega-1 of center for nilpotent p-group
From Groupprops
Statement
In a Nilpotent p-group (?) , any Minimal normal subgroup (?) is contained in the subgroup
(the first omega subgroup of the center of
). Thus, the Socle (?) of
is contained in
.
(in fact, something stronger is true: for a nilpotent p-group, the socle equals Omega-1 of the center).
Related facts
- Socle equals Omega-1 of center for nilpotent p-group
- Minimal normal implies central in nilpotent
- Minimal characteristic implies central in nilpotent
- Minimal characteristic implies contained in Omega-1 of center for nilpotent p-group