What is the additive group $\mathbb{Z}^0$? Is it the trivial group? I can't seem to find an answer to this online.
2026-04-02 12:48:36.1775134116
What is meant by $\mathbb{Z}^0$?
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The group $G^n$ consists of $n$-tuples with elements in $G$, or equivalently functions from a $n$-element set to $G$, with component-wise operations.
So then, $G^0$ would be the set of functions from the empty set to $G$. We have component-wise operations, but with no components to operate on that's irrelevant. There is only one empty function, and this becomes the trivial group of one element.