- #1
rsa58
- 85
- 0
Homework Statement
1- Sometimes my teacher writes the proof for when a set is a subgroup by saying the following: since e(identity) belongs to G then G is not empty. He then puts if a(b^(-1)) belongs to G then the rest of the conditions are satisfied. Why is this so? is it because if a and b belong to G then we can take a=e and we have the inverse. and then a(b^(-1))^(-1) belongs to G so ab belongs to G?
2- H is normal in G. m=(G) show a^m belongs to H for all a belonging to G. Proof: any aH belonging to G/H has the property that (aH)^m = e. And then the rest i get. my question is why is (aH)^m = e. Should G/H be cyclic for this to be the case? I know if we have a finite group then we can say a^m =e for some m in Z+. but yeah.
Homework Equations
The Attempt at a Solution
Last edited: