I'm having a bit of trouble with this problem:
Let phi: (G,*)->(H, . ) be a homomorphism.
If S is a subset of im(Phi), prove that the group S generates is a subgroup of im(Phi)
I don't know where to go with this....
Thanks in advance
"Also, do you consider to the intersection of all groups containing ?"
yes, the intersection of all subgroups containing S.
"But now I'm confused because you're talking about when earlier ? "
Is there a difference though? I mean what if I defined L = the image of Phi(G). Then S is a subset of L, prove that the group generated by the set S is a subgroup of L. Same question just reduced right?