# Semantic search

Center is characteristic, Characteristicity is centralizer-closed, Characteristicity is commutator-closed, Characteristicity is strongly intersection-closed, Characteristicity is strongly join-closed, Characteristicity is transitive, Cyclic subgroup is characteristic in dihedral group, Derived subgroup is characteristic, Every group is characteristic in itself, Finitary alternating group is characteristic in symmetric group, Finitary symmetric group is characteristic in symmetric group, Fully invariant implies characteristic, Isomorph-containing implies characteristic, Left-transitively complemented normal implies characteristic, Left-transitively permutable implies characteristic, Normality-preserving endomorphism-invariant implies characteristic, Self-centralizing and minimal normal implies characteristic, Special linear group is characteristic in general linear group, Subgroup-defining function value is characteristic, Trivial subgroup is characteristic