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In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order ''n'', every subgroup's order is a divisor of ''n'', and there is exactly one subgroup for each divisor.〔.〕 This result has been called the fundamental theorem of cyclic groups. ==Finite cyclic groups== For every finite group ''G'' of order ''n'', the following statements are equivalent: * ''G'' is cyclic. * For every divisor ''d'' of ''n'', ''G'' has exactly one subgroup of order ''d''. * For every divisor ''d'' of ''n'', ''G'' has at most one subgroup of order ''d''. This statement is known by various names such as characterization by subgroups. (See also cyclic group for some characterization.) There exist finite groups other than cyclic groups with the property that all proper subgroups are cyclic; the Klein group is an example. However, the Klein group has more than one subgroup of order 2, so it does not meet the conditions of the characterization. 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「Subgroups of cyclic groups」の詳細全文を読む スポンサード リンク
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