- Thread starter
- #1

Let $G$ be a group, and $\left \{ H_{i} \right \}_{i\in \mathbb{Z}}$ be an ascending chain of subgroups of $G$; that is, $H_{i}\subseteq H_{j}$ for $i\leqslant j$. Prove that $\bigcup _{i\in \mathbb{Z}}H_{i}$ is a subgroup of $G$.

I don't need the proof now. But can you show an example for me that the assertion fails to a set of subgroups that do not satisfy the ascending chain condition?

I don't need the proof now. But can you show an example for me that the assertion fails to a set of subgroups that do not satisfy the ascending chain condition?

Last edited by a moderator: