Prove that $D_4$ cannot be expressed as the internal direct product of two proper subgroups.
23077
Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
61235
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
146760
Prove that H is a subgroup of G
142101
A direct product of projective modules which is not projective
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
152589
How to show that if $G$ is union of three proper subgroups, then there is an epimorphism from $G$ to the Klein 4-group?
42096
Direct product of Sylow subgroups
128428
Why is the set of commutators not a subgroup?
11665
Show that $D_{12}$ is isomorphic to $D_6\times C_2$
35124
Can every non-simple group $G$ be written as a semidirect product?
8694
$A_4$ is not isomorphic to $D_6$
146028
$GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
14611
$A_4$ has no subgroup of order $6$?
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
83919
How to show $D_3\oplus D_4$ is not isomorphic to $D_{24}$?