Understanding Why $\mathbb{Q}^+$ Isn't a Cyclic Group Under Multiplication
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
9422
Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
57887
When are the product of cyclic groups also cyclic?
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
129239
Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
10606
Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result
142488
Galois Basic Question (Cyclic Order 4 Extension of Q cannot contain i)
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
95459
$\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.