query: Homomorphism from the alternating group $A_4$ to $\mathbb{Z}_3$
positive_passages.docid: 29453
positive_passages.text: An epimorphism from $S_{4}$ to $S_{3}$ having the kernel isomorphic to Klein four-group
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 5906
negative_passages.text: All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
negative_passages.docid: 119648
negative_passages.text: For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
negative_passages.docid: 129162
negative_passages.text: Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
negative_passages.docid: 146990
negative_passages.text: How to find the number of automorphisms on $\mathbb Z_2\times \mathbb Z_4$
negative_passages.docid: 21958
negative_passages.text: Splitting of conjugacy class in alternating group
negative_passages.docid: 133612
negative_passages.text: How many isomorphisms are there from $\Bbb Z_{12}$ to $\Bbb Z_{4} \oplus \Bbb Z_{3}$?
negative_passages.docid: 58108
negative_passages.text: The alternating group is generated by three-cycles
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: 90616
negative_passages.text: When is mapping $g$ to $g^{-1}$ a group homomorphism?
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 51695
negative_passages.text: Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
negative_passages.docid: 13764
negative_passages.text: Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
negative_passages.docid: 130081
negative_passages.text: Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
negative_passages.docid: 141265
negative_passages.text: Finding a normal and not normal subgroup of $S_3$