Talk:Existence of Unique Subgroup Generated by Subset/Singleton Generator

I'm puzzled as to the need for this proof by induction. The initial proof was all that was needed: to prove that any subgroup containing $a$ has $H$ as a subgroup. As $K$ is a group, it is closed and therefore $a^n \in K$. Job done. --prime mover (talk) 01:35, 23 May 2017 (EDT)