query: I have to show whether the groups $(\mathbb{C}, +, 0)$ and $(\mathbb{C} − \{0\}, \times, 1)$ are isomorphic.
positive_passages.docid: 25050
positive_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 157915
negative_passages.text: Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
negative_passages.docid: 136083
negative_passages.text: Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
negative_passages.docid: 81197
negative_passages.text: Why is $SO(3)\times SO(3)$ isomorphic to $SO(4)$?
negative_passages.docid: 6101
negative_passages.text: Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
negative_passages.docid: 88645
negative_passages.text: Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 61513
negative_passages.text: Prove that all cyclic groups of the same order are isomorphic
negative_passages.docid: 52556
negative_passages.text: Isomorphism of $S^1$.
negative_passages.docid: 100439
negative_passages.text: Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$
negative_passages.docid: 5996
negative_passages.text: Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
negative_passages.docid: 67772
negative_passages.text: How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
negative_passages.docid: 137011
negative_passages.text: showing $\psi: R\to \mathbb C$ is ring isomorphism.
negative_passages.docid: 26749
negative_passages.text: $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
negative_passages.docid: 146028
negative_passages.text: $GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
negative_passages.docid: 98765
negative_passages.text: Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
negative_passages.docid: 61732
negative_passages.text: Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
negative_passages.docid: 145000
negative_passages.text: Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?