# Semantic search

Center is normal, Central factor implies normal, Central implies normal, Characteristic implies normal, Commutator of a group and a subgroup implies normal, Cyclic normal Sylow subgroup for least prime divisor is central, Direct factor implies normal, Every group is normal in itself, Finitary symmetric group is normal in symmetric group, Normality is commutator-closed, Normality is strongly intersection-closed, Normality satisfies image condition, Normality satisfies intermediate subgroup condition, Potentially verbal implies normal, Pronormal and subnormal implies normal, Subgroup of index equal to least prime divisor of group order is normal, Subgroup of index two is normal, Trivial subgroup is normal