query: Are the two groups $\mathbb R$ and $\mathbb C$ isomorphic?
positive_passages.docid: 5996
positive_passages.text: Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
negative_passages.docid: 59995
negative_passages.text: Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.
negative_passages.docid: 61226
negative_passages.text: Group Structure on $\Bbb R$
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 37904
negative_passages.text: Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
negative_passages.docid: 107511
negative_passages.text: If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
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: 32428
negative_passages.text: Group homomorphisms and which of the following statements are true (NBHM-$2014$)
negative_passages.docid: 126098
negative_passages.text: Isomorphism of factor groups
negative_passages.docid: 150204
negative_passages.text: Isomorphisms between the groups $U(10), U(5)$ and $\mathbb{Z}/4\mathbb{Z}$
negative_passages.docid: 142352
negative_passages.text: how to prove $G_1$ and $G_2$ aren't isomorphic?
negative_passages.docid: 58009
negative_passages.text: How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
negative_passages.docid: 40400
negative_passages.text: Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$
negative_passages.docid: 158975
negative_passages.text: Isomorphism of centers of isomorphic groups
negative_passages.docid: 30236
negative_passages.text: isomorphic groups related in direct product.