# Semantic search

Artin's induction theorem, Brauer's induction theorem, Character orthogonality theorem, Clifford's theorem, Degree of irreducible representation divides index of abelian normal subgroup, Degree of irreducible representation divides order of group, Degree of irreducible representation need not divide index of abelian subgroup, Frobenius reciprocity, Isotypical-or-induced lemma, Maschke's averaging lemma, Schur's lemma, Some irreducible character vanishes on every conjugacy class, Splitting implies characters form a basis for space of class functions, Square of degree of irreducible representation need not divide group order, Sufficiently large implies character-separating, Sum of squares of degrees of irreducible representations equals order of group