# Coset representatives when a subgroup $H$ is not normal.

Let $$G$$ be a group and let $$H$$ be a subgroup of $$G$$.

If $$H$$ is normal then the set of all left coset representatives is the same as the set of all right coset representatives.

If $$H$$ is not normal, does there exist a set of left coset representatives which happens to also be a right coset representatives?

• Regardless of $H$ being normal or not, take $eH=He$, where $e$ is the identity. Dec 19 '19 at 3:20
• Not the intended meaning of the question :p Anything aside $\{e\}$ though? Dec 19 '19 at 3:21
• take something in the center of the group if the center is non-trivial. Dec 19 '19 at 3:22
• perhaps this will help you: math.stackexchange.com/questions/178186/… Dec 19 '19 at 3:24
• Dec 19 '19 at 4:13