- #1
gottfried
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Homework Statement
Let H be a subgroup of G
Prove xH=yH ⇔ x-1.y[itex]\in[/itex]H
Homework Equations
The Attempt at a Solution
If x.H = y.H then x,y[itex]\in[/itex]H
since H is a subgroup x-1,y-1[itex]\in[/itex]H
and the closure of H means x-1.y[itex]\in[/itex]H
Proving the reverse is my problem despite the fact that I'm sure is very easy but i just can't see it.
What I want to do is show that x-1.y[itex]\in[/itex]H implies x,y[itex]\in[/itex]H
In which case x.H=H=y.H.
How is the best way to show this?