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

up vote 0 down vote accepted

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

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In cryptography, $\mathbb{Z}^*_{n}$ is sometimes used to describe all of the multiplicative invertable elements of some zet $\mathbb{Z}_{n}$

http://en.wikipedia.org/wiki/Modular_multiplicative_inverse

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\mathbb {Z}_n^* is very commonly used (not just in cryptography) to denote the invertible elements in the group \mathbb {Z}_n. However, this does not seem to be what the question was asking. –  Ittay Weiss Nov 12 '12 at 8:29
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