query: Basic Abstract Algebra - Homomorphism
positive_passages.docid: 17178
positive_passages.text: Order of $\phi(g)$ divides the order of $g$
negative_passages.docid: 83710
negative_passages.text: Order of a homomorphism of groups
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: 57283
negative_passages.text: Extending Homomorphism into Algebraically Closed Field
negative_passages.docid: 144211
negative_passages.text: a second course in abstract algebra
negative_passages.docid: 105103
negative_passages.text: Automorphism from $\Bbb Q$ to $\Bbb Q$
negative_passages.docid: 100149
negative_passages.text: If there are injective homomorphisms between two groups in both directions, are they isomorphic?
negative_passages.docid: 42923
negative_passages.text: A Book for abstract Algebra
negative_passages.docid: 153291
negative_passages.text: Why a ring homomorphism from a local ring will not map a non-unit to a unit？
negative_passages.docid: 28252
negative_passages.text: How many homomorphisms are there from $\Bbb Z_{20}$ onto $\Bbb Z_{8}$? How many are there to $\Bbb Z_{8}$?
negative_passages.docid: 143451
negative_passages.text: Homomorphism from $(\Bbb Q,+)$ to a finite group
negative_passages.docid: 88930
negative_passages.text: Homomorphism between free groups
negative_passages.docid: 148881
negative_passages.text: Aut(GxH) isomorphic to Aut(G)xAut(H)
negative_passages.docid: 33455
negative_passages.text: Question on group homomorphisms involving the standard Z-basis
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: 89415
negative_passages.text: Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$
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.