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In mathematics, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups are finitely presented, and this makes them interesting from a computational point of view. ==Terminology== Equivalently, a group ''G'' is polycyclic if and only if it admits a subnormal series with cyclic factors, that is a finite set of subgroups, let's say ''G''0, ..., ''G''''n'' such that * ''G''0 coincides with ''G'' * ''G''''n'' is the trivial subgroup * ''G''''i''+1 is a normal subgroup of ''G''''i'' (for every ''i'' between 0 and ''n'' - 1) * and the quotient group ''G''''i'' / ''G''''i''+1 is a cyclic group (for every ''i'' between 0 and ''n'' - 1) A metacyclic group is a polycyclic group with ''n'' ≤ 2, or in other words an extension of a cyclic group by a cyclic group. 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「polycyclic group」の詳細全文を読む スポンサード リンク
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