扁頭科學 asked in 科學數學 · 9 years ago

代數學問題 Let H be a non-empty...

Let H be a non-empty subset of the group G. Prove that H is a subgroup of G if given a,b∈H, then a^-1b∈H.

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  • 9 years ago
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    欲證明(1) e∈H, and (2)ab∈H whenever a,b∈H. to claim that H is a subgroup.

    (1): let b=a ∈H then a^-1b=a^-1a=e∈H.

    (2): by (1) let b=e then a^-1∈H => If a, b ∈H, a^-1,b^-1∈H. Take c=a^-1, b=b∈H, since c^-1b∈H, [c^-1b=]ab∈H.

  • 9 years ago

    為什麼If a, b ∈H, a^-1,b^-1∈H

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