1. The problem statement, all variables and given/known data Suppose G is a group, H < G (H is a subgroup of G), and a is in G. Prove that a is in H iff <a> is a subset of H. 2. Relevant equations <a> is the set generated by a (a,aa,aa^-1,etc) 3. The attempt at a solution For some reason this seems too easy: 1. Suppose a is in H. Since H is a group, a^-1 is in H. Since H is a group aa, is in H (as is aa^-1, etc.) Thus <a> is a subset of H. 2. Suppose <a> is a subset of H. Obviously a is in H. And this completes the proof... or am I missing something?