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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 G
be a group and let H be a nonempty subset of G. If for all a and b in H, a b ^ is in H, then H is a subgroup of G.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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