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In mathematics, in the field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its successor. The series may be infinite. If the series is finite, then the subgroup is subnormal. Here are some properties of ascendant subgroups: * Every subnormal subgroup is ascendant; every ascendant subgroup is serial. * In a finite group, the properties of being ascendant and subnormal are equivalent. * An arbitrary intersection of ascendant subgroups is ascendant. * Given any subgroup, there is a minimal ascendant subgroup containing it. ==See also== * Descendant subgroup 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「Ascendant subgroup」の詳細全文を読む スポンサード リンク
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