query: Showing that a homomorphism between groups of units is surjective.
positive_passages.docid: 68728
positive_passages.text: Why does the natural ring homomorphism induce a surjective group homomorphism of units?
negative_passages.docid: 45792
negative_passages.text: Rigorous proof that surjectivity implies injectivity for finite sets
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: 134858
negative_passages.text: Abelian Group Homomorphism
negative_passages.docid: 54911
negative_passages.text: The preimage of a normal subgroup under a group homomorphism is normal
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: 150961
negative_passages.text: An example for a homomorphism that is not an automorphism
negative_passages.docid: 38691
negative_passages.text: Injectivity of Homomorphism in Localization
negative_passages.docid: 32428
negative_passages.text: Group homomorphisms and which of the following statements are true (NBHM-$2014$)
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: 3462
negative_passages.text: Proving a set of automorphisms of a group is a group under composition
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 7890
negative_passages.text: Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
negative_passages.docid: 46863
negative_passages.text: Show that $g$ is injective
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: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems