query: Is there an onto homomorphism $S_4\to S_3$
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: 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: 41294
negative_passages.text: Permutation module of $S_n$
negative_passages.docid: 5699
negative_passages.text: The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
negative_passages.docid: 83919
negative_passages.text: How to show $D_3\oplus D_4$ is not isomorphic to $D_{24}$?
negative_passages.docid: 59138
negative_passages.text: Subgroups of $S_4$ isomorpic to $S_2$
negative_passages.docid: 48818
negative_passages.text: Homomorphism of local rings
negative_passages.docid: 123419
negative_passages.text: Abstract algebra: homomorphism and an element of a prime order
negative_passages.docid: 126644
negative_passages.text: Simple module and homomorphisms
negative_passages.docid: 50130
negative_passages.text: $\operatorname{Aut}(V)$ is isomorphic to $S_3$
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: 88930
negative_passages.text: Homomorphism between free groups
negative_passages.docid: 77969
negative_passages.text: Question about proof for $S_4 \cong V_4 \rtimes S_3$
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
negative_passages.docid: 91129
negative_passages.text: Can there be an onto homomorphism from a ring without unity to a ring with unity?
negative_passages.docid: 642
negative_passages.text: Does a surjective ring homomorphism have to be surjective on the unit groups?
negative_passages.docid: 83710
negative_passages.text: Order of a homomorphism of groups