query: Two non-isomorphic modules that are isomorphic groups
positive_passages.docid: 151287
positive_passages.text: Isomorphic abelian groups which are not isomorphic R-modules
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 70658
negative_passages.text: Isomorphism between quotient modules
negative_passages.docid: 55778
negative_passages.text: Group theoretic meaning of natural isomorphisms between certain functors
negative_passages.docid: 75641
negative_passages.text: Is there a (f.g., free) module isomorphic to a quotient of itself?
negative_passages.docid: 30236
negative_passages.text: isomorphic groups related in direct product.
negative_passages.docid: 7010
negative_passages.text: Example of two non-isomorphic fields which embed inside each other
negative_passages.docid: 60925
negative_passages.text: Why these are isomorphic each other for given these rings?
negative_passages.docid: 47630
negative_passages.text: Endomorphisms of modules satisfying chain conditions and counterexamples.
negative_passages.docid: 85752
negative_passages.text: Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
negative_passages.docid: 62277
negative_passages.text: Cayley tables for two non-isomorphic groups of order 4.
negative_passages.docid: 137285
negative_passages.text: Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
negative_passages.docid: 88645
negative_passages.text: Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 128300
negative_passages.text: Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
negative_passages.docid: 93169
negative_passages.text: Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups