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Questions on the group-theoretic functionality of Mathematica.

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How to find all left cosets about a subgroup?

Since two left cosets $g\cdot H$ and $h \cdot H$ satisfies $g\cdot H= h \cdot H$ is equavalent to $ h^{-1}\cdot g\in H$,we set it as the equivalence relationships and use Gather. Gather[GroupElements[ …
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