query: Why $\gcd(12,30)$ equals the number of homomorphisms from $\Bbb Z_{12}$ to $\Bbb Z_{30}$?
positive_passages.docid: 141984
positive_passages.text: Find the number of homomorphisms between $\mathbb{Z}_m$ and $\mathbb{Z}_n$
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
negative_passages.docid: 32108
negative_passages.text: $ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
negative_passages.docid: 47824
negative_passages.text: Calculation of subgroups of $(Z_{12}, +)$
negative_passages.docid: 126930
negative_passages.text: Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
negative_passages.docid: 108691
negative_passages.text: Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
negative_passages.docid: 26661
negative_passages.text: Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
negative_passages.docid: 78852
negative_passages.text: If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
negative_passages.docid: 33455
negative_passages.text: Question on group homomorphisms involving the standard Z-basis
negative_passages.docid: 47623
negative_passages.text: The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
negative_passages.docid: 32278
negative_passages.text: Adjoining 1/2 to $\Bbb{Z}/12\Bbb{Z}$
negative_passages.docid: 40383
negative_passages.text: Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
negative_passages.docid: 72853
negative_passages.text: What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?
negative_passages.docid: 47720
negative_passages.text: Isomorphism from Natural numbers to the Odd Natural numbers
negative_passages.docid: 93017
negative_passages.text: Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
negative_passages.docid: 102938
negative_passages.text: $\Bbb F_2[X]$ modules with 8 elements
negative_passages.docid: 129162
negative_passages.text: Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$