query: Proving that a function is an automorphism
positive_passages.docid: 151699
positive_passages.text: Group of inner automorphisms of a group $G$
negative_passages.docid: 85768
negative_passages.text: The function $f:G \rightarrow G$ defined by $f(x)=x^2$ is a homomorphism iff G is abelian.
negative_passages.docid: 133083
negative_passages.text: Injectivity and surjectivity of a recursive function
negative_passages.docid: 46263
negative_passages.text: Automorphisms of infinite abelian groups
negative_passages.docid: 117151
negative_passages.text: Conformal automorphism of unit disk that interchanges two given points
negative_passages.docid: 69361
negative_passages.text: How do you find the automorphism?
negative_passages.docid: 101079
negative_passages.text: Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
negative_passages.docid: 30817
negative_passages.text: Is an automorphism of the field of real numbers the identity map?
negative_passages.docid: 133498
negative_passages.text: Show that Function Compositions Are Associative
negative_passages.docid: 26388
negative_passages.text: proof that function is constant
negative_passages.docid: 65977
negative_passages.text: Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
negative_passages.docid: 3606
negative_passages.text: Wild automorphisms of the complex numbers
negative_passages.docid: 10350
negative_passages.text: Automorphisms of the complex plane
negative_passages.docid: 113671
negative_passages.text: Frobenius Automorphism as a linear map
negative_passages.docid: 36980
negative_passages.text: Prove the third isomorphism theorem
negative_passages.docid: 14277
negative_passages.text: Proving $f(x)=x\cdot |x|$ is a bijection
negative_passages.docid: 147021
negative_passages.text: Proving a function is bounded