query: Is there a group $G$ such that $\mathrm{Aut}(G)\simeq (\mathbb{Q},+)$?
positive_passages.docid: 156549
positive_passages.text: Prove that there is no group $G$ s.t. $\operatorname{Aut}(G)=\mathbb{Q}$
negative_passages.docid: 129239
negative_passages.text: Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
negative_passages.docid: 93703
negative_passages.text: Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$
negative_passages.docid: 51334
negative_passages.text: Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
negative_passages.docid: 143451
negative_passages.text: Homomorphism from $(\Bbb Q,+)$ to a finite group
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 43759
negative_passages.text: Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
negative_passages.docid: 149578
negative_passages.text: Subgroups of $(\mathbb Z_n,+)$
negative_passages.docid: 150199
negative_passages.text: How to prove for a finite group that $|\langle g \rangle|=o(g)$?
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 52121
negative_passages.text: Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
negative_passages.docid: 127198
negative_passages.text: What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
negative_passages.docid: 39469
negative_passages.text: If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
negative_passages.docid: 30676
negative_passages.text: $G'$ and the product of all the elements in an odd order group
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: 157915
negative_passages.text: Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
negative_passages.docid: 91287
negative_passages.text: Is $G/pG$ is a $p$-group?