query: Why is the multiplicative group of a finite field cyclic?
positive_passages.docid: 8623
positive_passages.text: Finite subgroups of the multiplicative group of a field are cyclic
negative_passages.docid: 14528
negative_passages.text: Proof that all abelian simple groups are cyclic groups of prime order
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 139499
negative_passages.text: The algebraic closure of a finite field and its Galois group
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: 54453
negative_passages.text: Finite abelian $p$-group with only one subgroup size $p$ is cyclic
negative_passages.docid: 126089
negative_passages.text: Showing $U(20)$ is not cyclic: Is my proof correct?
negative_passages.docid: 10760
negative_passages.text: Why is the product of all units of a finite field equal to $-1$?
negative_passages.docid: 71608
negative_passages.text: A property of finite field of order $2^n$
negative_passages.docid: 23394
negative_passages.text: If $G/Z(G)$ is cyclic, then $G$ is abelian
negative_passages.docid: 131706
negative_passages.text: Is my proof that $U_{pq}$ is not cyclic if $p$ and $q$ are distinct odd primes correct?
negative_passages.docid: 78696
negative_passages.text: Galois group of the product of two fields being the product of Galois groups?
negative_passages.docid: 123219
negative_passages.text: What is multiplicative group $\bar{\mathbb{F}}_p^*$ for algebraic closure $\bar{\mathbb{F}}_p$ of $\mathbb{F}_p$ where $p$ is prime?
negative_passages.docid: 152954
negative_passages.text: Extensions of finite cyclic groups
negative_passages.docid: 68733
negative_passages.text: If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
negative_passages.docid: 142894
negative_passages.text: Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
negative_passages.docid: 151619
negative_passages.text: A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic