Show that the set of non zero rationals is not a cyclic group under multiplication.
119545
Nonzero rationals under multiplication are not a cyclic group
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
92298
The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
102622
K is a subgroup of G. Show that K is not a normal subgroup
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
40663
$a_1 a_1', a_2 a_2', ..., a_n a_n'$ is not a reduced modulo system $\mod p$.
125604
Proof that $\mathbb{Z}$ has no zero divisors