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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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    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 $\mathbb{Z_2}$.