query: Every group of order 111 is cyclic. (True or False)
positive_passages.docid: 86025
positive_passages.text: Nonabelian semidirect products of order $pq$?
negative_passages.docid: 155219
negative_passages.text: Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
negative_passages.docid: 58014
negative_passages.text: Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.
negative_passages.docid: 104460
negative_passages.text: When a group is cyclic
negative_passages.docid: 84823
negative_passages.text: When is the group of units in $\mathbb{Z}_n$ cyclic?
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 60075
negative_passages.text: Does there exist an $n$ such that all groups of order $n$ are Abelian?
negative_passages.docid: 24970
negative_passages.text: Only two groups of order $10$: $C_{10}$ and $D_{10}$
negative_passages.docid: 58397
negative_passages.text: Every cyclic group with order > 2 has at least 2 distinct generators
negative_passages.docid: 128899
negative_passages.text: How to find all generators for a cyclic group of order $n$?
negative_passages.docid: 5223
negative_passages.text: $\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
negative_passages.docid: 84501
negative_passages.text: Proof involving Cyclic group, generator and GCD
negative_passages.docid: 144258
negative_passages.text: How to show a group is cyclic?
negative_passages.docid: 26398
negative_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?
negative_passages.docid: 152662
negative_passages.text: Proving that any finite cyclic group of order $n$ is isomorphic to $$