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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? – wj32 Nov 12 '12 at 6:33
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...) – Mariano Suárez-Alvarez Nov 12 '12 at 6:34
@wj32, the identity of what? Notice that the question is «what is the codomain?» – Mariano Suárez-Alvarez Nov 12 '12 at 6:34
@MarianoSuárez-Alvarez: Oh yes, I didn't see that. Still, it works. – wj32 Nov 12 '12 at 6:35
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. – Dan Shved Nov 12 '12 at 7:28
up vote 0 down vote accepted

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

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