(related to Problem: Verifying Subgroup Properties)

There are two possibilities to show that a non-empty subset $H$ of a group $(G,\ast)$ is its subgroup. Both possibilities are equivalent. Which possibility you choose is more or less a matter of taste and of simplicity.

$(1)$ Verify the subgroup properties

$(2)$ Verify the subgroup criterion.

I.e. show that $a\ast b^{-1}\in H$ for all $a,b\in H.$

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