MULTIPLICATIVE GROUPS IN Zm
نویسنده
چکیده
Our goal will be to find subsets of Zm that form groups under the operation of multiplication modulo m. By utilizing the isomorphism Zm ∼= Zn ⊕ Zk, we will find multiplicative groups contained in Zn ⊕ Zk and then map these back to Zm. In particular, if m = nk with gcd(n, k) = 1, our objective is to find particular multiplicative subsets of Zn × Zk that are groups and whose first coordinate is a projection onto U(n). We will give a method to calculate the total number of these subsets, and identify the elements of which they are composed.
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