Let G be a group, and let H be normal in G. Prove that every subgroups of G/H is of the form K/H, where K is a subgroup of G with .
My proof so far:
Let , let X be a subgroup of G/H. By a theorem, is a subgroup of G.
Any help from here?
Thanks.
Let G be a group, and let H be normal in G. Prove that every subgroups of G/H is of the form K/H, where K is a subgroup of G with .
My proof so far:
Let , let X be a subgroup of G/H. By a theorem, is a subgroup of G.
Any help from here?
Thanks.