Is $D_{2n}$ isomorphic to $D_n \times \Bbb{Z}_2$ for all $n$? For all odd $n$?
6453
Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
154754
Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
35660
Elements of order 2 in $D_{2n}$
32302
Neukirch’s Number Theory – why is $ℂ \otimes_ℚ K → K_ℂ,~z \otimes a ↦ (j(z)a)_τ$ an isomorphism?
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
35626
Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
85752
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
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
133612
How many isomorphisms are there from $\Bbb Z_{12}$ to $\Bbb Z_{4} \oplus \Bbb Z_{3}$?
81197
Why is $SO(3)\times SO(3)$ isomorphic to $SO(4)$?
114394
Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
29003
Is the dihedral group $D_n$ nilpotent? solvable?
141843
n-dimensional vector space isomorphic to the n-th product of a field as abelian groups