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ripcity4545
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Homework Statement
Prove that Z sub n is cyclic. (I can't find the subscript, but it should be the set of all integers, subscript n.)
Homework Equations
Let (G,*) be a group. A group G is cyclic if there exists an element x in G such that G = {(x^n); n exists in Z.}(Z is the set of all integers)
The Attempt at a Solution
* is a binary operation, and for my purposes, is either additive (+) or multiplicative (x).
Multiplicative does not work because the multiplicative inverse of, say, 2 is not an integer. So the operation must be additive. So I can rewrite the equation for (G,+) as:
G = {nx; n exists in Z}
but that's where I get stuck. Thanks for the help!
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