# This is Daily Work 14.

Let $$\phi \colon G \to H$$ be an isomorphism between the groups $$G$$ and $$H$$.
Which of the following observations would guarantee that $$G$$ is not isomorphic to $$H$$ ?
If $$a \in G$$ is not the identity element, and $$H$$ is a subgroup of $$G$$, which of the following sets is guaranteed to also be a subgroup of $$G$$?