Wording of coset

Question

Given a group $G$, a subgroup $H$ of $G$, and $a\in G$, we have the left coset $aH$. What is the usual correct complete wording of it?

• $aH$ is $H$-left coset of $a$ in $G$
• $aH$ is left coset of $a$ respect $H$ in $G$
• $aH$ is ...?

it's more an English question...

Answer 1

According to Coset Wiki page

$gH$ = { $gh$ : $h$ an element of $H$ } is the left coset of $H$ in $G$ with respect to $g$,