$\mathbb{Z}[G]$ isomorphic to $\mathbb{Z}[H]$ then what can be said about $G$ and $H$?
6385
Minimal counterexamples of the isomorphism problem for integral group rings
13761
Automorphisms in $\mathbb{Z}_n$
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
120183
Prove that $S_3\times\mathbb{Z}_2$ is isomorphic to $D_6$
23279
Group Theory Isomorphism
2153
How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
114394
Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
33455
Question on group homomorphisms involving the standard Z-basis
154847
homomorphism from $S_3$ to $\mathbb Z/3\mathbb Z$
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
120035
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
97009
Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?
98587
$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
12110
How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$