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left coset

For $H \le G$ and $g \in G$ , the set $gH = \{gh : h \in H\}$ -- every element of $H$ multiplied by $g$ on the left.

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Examples

In $S_3$ with $H=\{e,(1\,2)\}$ , the left coset $(1\,2\,3)H=\{(1\,2\,3),(1\,2\,3)(1\,2)\}$ .