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.
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Originally Posted by tttcomrader 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. I have no idea what it means "of the form K/H" Given the canonical homormorphism . If is a subgroup, i.e. then, .
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