Nilpotent normal subgroup
= Nilpotent normal subgroup
A <normal subgroup> which is a <nilpotent group>. In a <finite group> its unique <Sylow subgroups> are <characteristic subgroups> and hence normal in the ambient group. Products of <nilpotent normal subgroups> are <nilpotent groups>: their normal Sylow subgroups of different prime characteristics commute.