Let $G$ be a group with operation written multiplicatively, let $H \le G$ be a subgroup, and let $g \in G$. Define the left coset $gH := \{gh : h \in H\}$ and the right coset $Hg := \{hg : h \in H\}$. The maps
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\begin{align*}
L_g: H &\to gH \\
h &\mapsto gh
\end{align*}
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and
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\begin{align*}
R_g: H &\to Hg \\
h &\mapsto hg
\end{align*}
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are bijections. Consequently, if the relevant cardinalities are finite, then $|gH| = |H|$ and $|Hg| = |H|$.