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Cosets and Subgroups

Let G = RxR (R is the real numbers) with addition (x,y) + (x', y') = (x+x', y+y'). Let H be the line y=mx through the origin: H = {(x,mx)such that x belongs to R (R is real numbers). Show that H is a subgroup of G and describe the cosets H + (a,b) geometrically.

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To show H is a subgroup of G, we only need to show h1-h2 is in H for any h1,h2 in ...

Solution Summary

This is a proof regarding cosets and subgroups.