Quantcast
Channel: Are Cosets Isomorphic to One Another - Mathematics Stack Exchange
Viewing all articles
Browse latest Browse all 3

Are Cosets Isomorphic to One Another

0
0

A basic question, I seem to be struggling with the concept of quotient groups and cosets.

Suppose $G$ is a group, and $N$ is a normal subgroup.

I know that is $x$ and $y$ are in the same coset of $G/N$, then $xN = yN$.

I also know that cosets are either disjoint or equivalent, $G/N$ is the set of cosets. Also, $G$ can be written as a disjoint union of the cosets.

Is it correct that all cosets are isomorphic to $N$, since they are of the form $xN$ for some $x \in G$?

Or is it possible for more elements of $G$ to be in one coset than in another?


Viewing all articles
Browse latest Browse all 3

Latest Images

Trending Articles





Latest Images