# Semantic search

Every group is normal in itself, Normality is commutator-closed, Normality is strongly UL-intersection-closed, Normality is strongly intersection-closed, Normality is strongly join-closed, Normality is upper join-closed, Normality satisfies image condition, Normality satisfies intermediate subgroup condition, Normality satisfies lower central series condition, Normality satisfies partition difference condition, Trivial subgroup is normal