Show that $Z\times Z$ is not cyclic...
90239
$\mathbb{Z} \times \mathbb{Z}$ is cyclic.
13734
Show that every group of prime order is cyclic
92430
Show that the group is cyclic.
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
99726
Proving that a function is not a contraction
33628
Prove that $\sin(\sqrt x)$ not periodic
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
87848
Formal proof for $(-1) \times (-1) = 1$
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
11259
Prove $R\times S$ is not an integral domain
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
78564
Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
36011
Show that the product of two consecutive natural numbers is never a square.