New posts in Quotient Group

Is this explanation of normal subgroups and quotient groups correct?

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

The order of elements in infinite quotient groups

Let $\varphi : G \rightarrow G/N$. Prove/Dis-prove that there exists a right inverse of $\varphi$ that is *homomorphic*.

How is the concept of $\Bbb Z/2\Bbb Z$ extended to $\Bbb N/2\Bbb N$? Is $\Bbb N/2\Bbb N$ ambiguous?

Computing the index $\left(\mathbb Z\left[\frac{1+\sqrt{5}}{2}\right]:\mathbb Z \left[\sqrt{5}\right]\right)$?

Is R/Z isomorphic to R/2Z?

Why in Quotient Group we need normal subgroup?

Why is the fact that a quotient group is a group relevant?

Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$