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Is pre-superscript a standard notation for something? I've encountered it in the following:

$$(a,g)(b,h) = (a + {}^gb + f(g,h), gh).$$

This was given in relation to a formula for the multiplication on the abelian set $A$ with extension $G$ as $A$ X $G$.

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${}^g b$ is, in general, shortand for $g$ acting on $b$ from the left. Often, this means the left conjugation action $gbg^{-1}$ (as opposed to $b^g = g^{-1} bg$, the right conjugation action). If $G$ and $A$ are separate groups, though, and $G$ has a distinguished action on $A$, then ${}^gb$ might be used instead of $g \cdot b$ in this action.


I hope this helps ^_^

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