query: How many group homomorphisms are there from $(\mathbb{Z}, +)$ to $(\mathbb{Z}_4, +_4)$?
positive_passages.docid: 18343
positive_passages.text: Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 121034
negative_passages.text: Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
negative_passages.docid: 159005
negative_passages.text: Finding all homomorphisms between two groups - couple of questions
negative_passages.docid: 29453
negative_passages.text: An epimorphism from $S_{4}$ to $S_{3}$ having the kernel isomorphic to Klein four-group
negative_passages.docid: 41231
negative_passages.text: Subgroups of (Z,+) of order n
negative_passages.docid: 62277
negative_passages.text: Cayley tables for two non-isomorphic groups of order 4.
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
negative_passages.docid: 13761
negative_passages.text: Automorphisms in $\mathbb{Z}_n$
negative_passages.docid: 84823
negative_passages.text: When is the group of units in $\mathbb{Z}_n$ cyclic?
negative_passages.docid: 5906
negative_passages.text: All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
negative_passages.docid: 1558
negative_passages.text: Number of homomorphisms between two cyclic groups.
negative_passages.docid: 26661
negative_passages.text: Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 3829
negative_passages.text: Number of automorphisms of a direct product of two cyclic $p$-groups
negative_passages.docid: 933
negative_passages.text: How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
negative_passages.docid: 40400
negative_passages.text: Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$