query: Are all group homorphisms of the reals also linear transformations?
positive_passages.docid: 27524
positive_passages.text: Map from real numbers to real numbers as abelian groups
negative_passages.docid: 149029
negative_passages.text: 3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
negative_passages.docid: 43326
negative_passages.text: Can every group be represented by a group of matrices?
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 121257
negative_passages.text: Image of Homomorphism of Lie groups
negative_passages.docid: 64372
negative_passages.text: Do the isomorphism's of groups form an equivalence relation on the class of all groups?
negative_passages.docid: 2153
negative_passages.text: How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
negative_passages.docid: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 76586
negative_passages.text: How to prove that linear transformations transforms lines into lines
negative_passages.docid: 150961
negative_passages.text: An example for a homomorphism that is not an automorphism
negative_passages.docid: 27728
negative_passages.text: Question on a homomorphism of a set G.
negative_passages.docid: 135855
negative_passages.text: Prove the group of all real translations and all glide reflections with axis$R$ is isomorphic to $\{1,-1\}\times \mathbb R$
negative_passages.docid: 40069
negative_passages.text: The image of a homomorphism is a group?
negative_passages.docid: 33868
negative_passages.text: A transformation between two free group actions.
negative_passages.docid: 18379
negative_passages.text: Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
negative_passages.docid: 34700
negative_passages.text: Proving that the matrix exponential map is surjective onto the general linear group
negative_passages.docid: 131480
negative_passages.text: Proof that composition of invertible linear transformations is invertible (without determinants)