Prove that the integers modulo 8 is not an internal direct product of two proper subgroups.
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
16172
My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
23077
Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
79425
Prove the direct product of nonzero complex numbers under multiplication.
158364
Are there uncountably many $A\in M_3 (\mathbb {R})$ such that $A^8=I $?
39096
Primitive elements of GF(8)
5741
Direct product of abelian groups
129937
How to prove that $A_5$ has no subgroup of order 30?
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
14447
Direct proof that $\pi$ is not constructible
61235
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
39965
Partition of $\mathbb{Z}_8$ into cosets of Ker(θ)
124864
A not free $\mathbb{Z}$-module
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.