query: Are these two infinite groups isomorphic?
positive_passages.docid: 142352
positive_passages.text: how to prove $G_1$ and $G_2$ aren't isomorphic?
negative_passages.docid: 146969
negative_passages.text: Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
negative_passages.docid: 81238
negative_passages.text: Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
negative_passages.docid: 123677
negative_passages.text: Normal subgroups of infinite symmetric group
negative_passages.docid: 139835
negative_passages.text: Every Finite Group is Isomorphic to a Subgroup of $A_n$
negative_passages.docid: 2254
negative_passages.text: Finite group with isomorphic normal subgroups and non-isomorphic quotients?
negative_passages.docid: 128692
negative_passages.text: Example of an infinite group where every element except identity has order 2
negative_passages.docid: 47617
negative_passages.text: Are groups with all the same Hom sets already isomorphic?
negative_passages.docid: 112993
negative_passages.text: Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
negative_passages.docid: 120288
negative_passages.text: Semigroup isomorphism
negative_passages.docid: 157040
negative_passages.text: For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$?
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
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: 133954
negative_passages.text: Does every infinite group have a maximal subgroup?
negative_passages.docid: 151287
negative_passages.text: Isomorphic abelian groups which are not isomorphic R-modules
negative_passages.docid: 23579
negative_passages.text: If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
negative_passages.docid: 10816
negative_passages.text: Infinitely generated subgroup of a finitely one (weird)