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Subgroup test : ウィキペディア英語版 | Subgroup test In abstract algebra, the one-step subgroup test is a theorem that states that for any group, a nonempty subset of that group is itself a group if the inverse of any element in the subset multiplied with any other element in the subset is also in the subset. The two-step subgroup test is a similar theorem which requires the subset to be closed under the operation and taking of inverses. ==One-step subgroup test==
Let be a group and let be a nonempty subset of . If for all and in , is in , then is a subgroup of .
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「Subgroup test」の詳細全文を読む
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