Let H be a normal subgroup of G. Let K be a subgroup of G/H and...

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Let H be a normal subgroup of G. Let K be a subgroup of G/H and set K = {g €G |gH E K}. (a) Show that K is a subgroup of G containing H. (b) Show thatK is a normal subgroup of G if and only if K is a normal subgroup of G/H. Let H be a normal subgroup of G. Let K be a subgroup of G/H and set K = {g €G |gH E K}. (a) Show that K is a subgroup of G containing H. (b) Show thatK is a normal subgroup of G if and only if K is a normal subgroup of G/H.

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