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No mention of requiring the identity element to be a member of the subgroup. |
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Let <math>G
</math> be a group and let <math>H</math> be a nonempty subset of <math>G</math>, where <math>H</math> contains the identity element from <math>G</math>. If for all <math>a</math> and <math>b</math> in <math>H</math>, <math>a b ^{-1}</math> is in <math>H</math>, then <math>H</math> is a subgroup of <math>G</math>.
===Proof===
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