$\textbf{Cosets of a group}$
Let $(G,\cdot )$ be a group and $(H,\cdot )$ a subgroup of $G$. For fixed $g\in G$, the left coset is $$gH=\{g\cdot h :h\in H\}$$ and the right coset is $$Hg=\{h\cdot g:h\in H\}.$$
The set of all left cosets is denoted by $G/H\coloneqq\{gH:g\in G\}$ and the set of all right cosets is denoted by $H\backslash G\coloneqq\{Hg:g\in G\}$.
$\textbf{Cosets of a group}$
Let $(G,\cdot )$ be a group and $(H,\cdot )$ a subgroup of $G$. For fixed $g\in G$, the left coset is $$gH=\{g\cdot h :h\in H\}$$ and the right coset is $$Hg=\{h\cdot g:h\in H\}.$$
The set of all left cosets is denoted by $G/H\coloneqq\{gH:g\in G\}$ and the set of all right cosets is denoted by $H\backslash G\coloneqq\{Hg:g\in G\}$.
copied
𝐂𝐨𝐬𝐞𝐭𝐬 𝐨𝐟 𝐚 𝐠𝐫𝐨𝐮𝐩
Let (𝐺,⋅) be a group and (𝐻,⋅) a subgroup of 𝐺. For fixed 𝑔∈𝐺, the left coset is
𝑔𝐻={𝑔⋅ℎ:ℎ∈𝐻}
and the right coset is
𝐻𝑔={ℎ⋅𝑔:ℎ∈𝐻}.
The set of all left cosets is denoted by 𝐺/𝐻≔{𝑔𝐻:𝑔∈𝐺} and the set of all right cosets is denoted by 𝐻\𝐺≔{𝐻𝑔:𝑔∈𝐺}.