I have three problems I wasn't able to solve by myself.
1) Is ( ) finitely generated group? Is it free?
2) Is free Abelian group?
3) Is free group?
I know that in order to check whether a group is finitely generated, I have to find a finite set that generates it, or prove it doesn't exist, but I can't do either.
Also, to check whether something is a free group, I would have to find its basis.
For example, is the basis of ?
I'm really lost, please help.