query: Is a field with cyclic multiplicative group necessarily finite?
positive_passages.docid: 21079
positive_passages.text: Why must a field whose a group of units is cyclic be finite?
negative_passages.docid: 84
negative_passages.text: For what $n$ is $U_n$ cyclic?
negative_passages.docid: 79725
negative_passages.text: Fields of arbitrary cardinality
negative_passages.docid: 154318
negative_passages.text: Can a field be isomorphic to its subfield?
negative_passages.docid: 98145
negative_passages.text: If $G$ is cyclic then $G/H$ is cyclic?
negative_passages.docid: 152954
negative_passages.text: Extensions of finite cyclic groups
negative_passages.docid: 24168
negative_passages.text: A characterisation of quadratic extensions contained in cyclic extensions of degree 4
negative_passages.docid: 99788
negative_passages.text: Why does a multiplicative subgroup of a field have to be cyclic?
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 106123
negative_passages.text: Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
negative_passages.docid: 109801
negative_passages.text: multiplicative group of infinite fields
negative_passages.docid: 118849
negative_passages.text: If a cyclic group has an element of infinite order, how many elements of finite order does it have?
negative_passages.docid: 64408
negative_passages.text: Subgroup of $\mathbb{Q}$ with finite index
negative_passages.docid: 107454
negative_passages.text: Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
negative_passages.docid: 116594
negative_passages.text: Finite fields are isomorphic
negative_passages.docid: 124455
negative_passages.text: Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
negative_passages.docid: 155219
negative_passages.text: Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.