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Let G be any group that has a subgroup H. Let g ∈ G, and let gH denote the left coset of H with representative g. Explain why g ∈ gH always.

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ShahzadAli1idn

Answer:

Hello!

I have make it shorter and easy to understand.

Step-by-step explanation:

To show that g ∈ g H, note that the left coset g H is defined as {gh | h ∈ H} . If you choose h to be the identity element e ∈ H, then g can be written as g . e . Since e ∈ H , this means g ∈ g H.

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