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In the mathematical field of group theory, a subgroup ''H'' of a given group ''G'' is a serial subgroup of ''G'' if there is a chain ''C'' of subgroups of ''G'' extending from ''H'' to ''G'' such that for consecutive subgroups ''X'' and ''Y'' in ''C'', ''X'' is a normal subgroup of ''Y''. The relation is written ''H ser G'' or ''H is serial in G''. If the chain is finite between ''H'' and ''G'', then ''H'' is a subnormal subgroup of ''G''. Then every subnormal subgroup of ''G'' is serial. If the chain ''C'' is well-ordered and ascending, then ''H'' is an ascendant subgroup of ''G''; if descending, then ''H'' is an descendant subgroup of ''G''. If ''G'' is a locally finite group, then the set of all serial subgroups of ''G'' form a complete sublattice in the lattice of all normal subgroups of ''G''.〔 ==See also== *Characteristic subgroup *Normal closure *Normal core 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「Serial subgroup」の詳細全文を読む スポンサード リンク
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