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The following is question I am being asked:

Find a homomorphism from the group $(D_3, \circ)$ of all symmetries of the equilateral triangle to the group $\bf{Z}^*$.

But what algebraic structure could the group $\bf{Z}^*$ be referring to here? Could this be $(\mathbb{Z}, +)$ or the multiplicative group of integers modular some $n \in \mathbb{N}$? I am trying to determine whether this is an ambiguous question or whether I am missing something.

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    Why not send everything to the identity?2012-11-12
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    Why don't you ask whoever asked you the question? They probably know what they meant! (If it is a book, then the notation is probably explained somewhere...)2012-11-12
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    @wj32, the identity of what? Notice that the question is «what is the codomain?»2012-11-12
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    @MarianoSuárez-Alvarez: Oh yes, I didn't see that. Still, it works.2012-11-12
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    Is it not the dual group? (of group homomorphisms from $\mathbb{Z}$ to $\mathbb{C}$\{$0$})2012-11-12
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    I've seen people use $\mathbb{Z}^*$ for the group $\{-1, 1\}$ under multiplication. This could be it, but you should really ask the author of the problem.2012-11-12
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    So the question is, what algebraic structure does $\bf{Z}$ denote? If it is taken to be a ring, then $\bf{Z}^{\ast}$ is most likely the group of units. If it is a group, then $\bf{Z}^{\ast}$ is likely to be the dual group.2012-11-12

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The algebraic structure turned out to be $\mathbb{Z_2}$.