- #1
vwishndaetr
- 87
- 0
Question:
Prove the following properties of cosets.
Given:
Let H be a subgroup and let a and b be elements of G.
[tex] H\leq\ G [/tex]
Statement:
[tex] aH=bH \ if\ and\ only\ if\ a^{-1}b\ \epsilon\ H [/tex]
The statement is what I have to prove.
My issue is I don't know how to start off the problem. When I first looked at the statement. I wanted to say that it is only true when a=b. But there is not talk of the groups being abelian. So what I thought was a start to some thinking, did not take me very far.
Prove the following properties of cosets.
Given:
Let H be a subgroup and let a and b be elements of G.
[tex] H\leq\ G [/tex]
Statement:
[tex] aH=bH \ if\ and\ only\ if\ a^{-1}b\ \epsilon\ H [/tex]
The statement is what I have to prove.
My issue is I don't know how to start off the problem. When I first looked at the statement. I wanted to say that it is only true when a=b. But there is not talk of the groups being abelian. So what I thought was a start to some thinking, did not take me very far.