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In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group. Because conjugation is an automorphism, every characteristic subgroup is normal, though not every normal subgroup is characteristic. Examples of characteristic subgroups include the commutator subgroup and the center of a group. == Definitions == A characteristic subgroup of a group ''G'' is a subgroup ''H'' that is invariant under each automorphism of ''G''. That is, : for every automorphism ''φ'' of ''G'' (where ''φ''(''H'') denotes the image of ''H'' under ''φ''). The statement “''H'' is a characteristic subgroup of ''G''” is written : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「characteristic subgroup」の詳細全文を読む スポンサード リンク
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