What would the notation G/H mean in terms of groups and subgroups?

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What would G/H mean in terms of subgroups? Would it most likely mean The compliment group of H in G?

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2 Answers

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If $H$ is normal in $G$, it means the quotient group. In the more general subgroup case, it could just mean the set of (left) cosets of $H$ in $G$.

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If $H$ is a normal subgroup of $G$, this is the quotient group: the set of cosets $$ \{ gH : g \in G \}, $$ equipped with multiplication $$ g_1 H \cdot g_2 H = (g_1 g_2) H. $$ (Obviously you have to check everything here is well-defined.)

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