Let G = GL(2,R) and let K be a subgroup of R*. Prove that H = {A ∈ G| det A ∈ K} is a normal subgroup of G.
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A subgroup is said to be normal iff we have So take it is a group and therefore invertible so but consider for any we would have: so we see that for any and for all we get . This shows thus it is normal.
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