Let G = GL(2,R) and let K be a subgroup ofR*. Prove that H = {A ∈ G| det A ∈ K} is a normal subgroup of G.

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- April 22nd 2009, 03:44 PMo&apartyrockNormal Subgroups and Factor Groups
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. - April 22nd 2009, 04:00 PMGammaNormal
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.