query: Prove, that the multiplicative group of a finite field is cyclic.
positive_passages.docid: 126590
positive_passages.text: Why is the multiplicative group of a finite field cyclic?
negative_passages.docid: 7967
negative_passages.text: Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
negative_passages.docid: 150007
negative_passages.text: Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group.
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: 90332
negative_passages.text: Prove that that $U(n)$ is an abelian group.
negative_passages.docid: 152662
negative_passages.text: Proving that any finite cyclic group of order $n$ is isomorphic to $$
negative_passages.docid: 84
negative_passages.text: For what $n$ is $U_n$ cyclic?
negative_passages.docid: 84823
negative_passages.text: When is the group of units in $\mathbb{Z}_n$ cyclic?
negative_passages.docid: 118610
negative_passages.text: Are all extensions of finite fields cyclic?
negative_passages.docid: 69046
negative_passages.text: Proof of $\mathbb{Q}$ is not cyclic
negative_passages.docid: 20161
negative_passages.text: Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
negative_passages.docid: 90239
negative_passages.text: $\mathbb{Z} \times \mathbb{Z}$ is cyclic.
negative_passages.docid: 126089
negative_passages.text: Showing $U(20)$ is not cyclic: Is my proof correct?
negative_passages.docid: 2104
negative_passages.text: Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
negative_passages.docid: 2304
negative_passages.text: What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 61394
negative_passages.text: The product of finitely many cyclic groups is cyclic