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Abelian implies every subgroup is potentially characteristic, Artin's induction theorem, Brauer's induction theorem, Central implies image-potentially characteristic, Central implies potentially characteristic, 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, Engel's theorem, Extensible equals inner, Finite NIPC theorem, Finite-characteristic-semidirectly extensible implies linearly pushforwardable over prime field, Finite-extensible endomorphism implies trivial or automorphism, Finite-extensible implies class-preserving, Frobenius reciprocity, Fundamental theorem of Galois theory, Hilbert's theorem 90, Isotypical-or-induced lemma, Kernel of a characteristic action on an abelian group with which it is characteristic in the direct product implies potentially characteristic, Lie's theorem, Maschke's averaging lemma, Mazur's theorem, Mordell-Weil theorem, Nagell-Lutz theorem, Nilpotent implies every normal subgroup is potentially characteristic, No nontrivial abelian normal p-subgroup for some prime p implies every normal subgroup is strongly image-potentially characteristic, No nontrivial abelian normal p-subgroup for some prime p implies every p-divisible normal subgroup is potentially characteristic, Periodic normal implies image-potentially characteristic, Periodic normal implies potentially characteristic, Perlis-Walker theorem, Pushforwardable equals inner, Quotient-pullbackable equals inner, Representation pullbackability theorem, 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, Sylow's theorem, Three subgroup lemma, Whitcomb-Jackson theorem, Witt's identity