How do I show that both the additive and multiplicative groups of an infinite field are non-cyclic?
21079
Why must a field whose a group of units is cyclic be finite?
61084
Examples of non-isomorphic fields with isomorphic group of units and additive group structure
8623
Finite subgroups of the multiplicative group of a field are cyclic
92430
Show that the group is cyclic.
126590
Why is the multiplicative group of a finite field cyclic?
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
99788
Why does a multiplicative subgroup of a field have to be cyclic?
147574
Prove of a finite cyclic group of order $n$ is isomorphic tto $(\mathbb Z_n,+)$.
76504
Non-trivial cyclic group with unique generator
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
45958
Proof that the Euler characteristic is additive
92677
Infinite algebraic extension of a finite field
120401
Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
118610
Are all extensions of finite fields cyclic?
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
71035
Non abelian subgroup of a abelian group.