Is the group $G$ always isomorphic to the group $G/N \times N$?
137949
If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$?
120155
How to show that this group presentation is isomorphic to dihedral group?
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
107687
How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
145000
Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?
64372
Do the isomorphism's of groups form an equivalence relation on the class of all groups?
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
23279
Group Theory Isomorphism
109596
Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
100439
Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?