query: Can we conclude that this group is cyclic?
positive_passages.docid: 2104
positive_passages.text: Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
negative_passages.docid: 84
negative_passages.text: For what $n$ is $U_n$ cyclic?
negative_passages.docid: 135710
negative_passages.text: Cyclic Automorphism group
negative_passages.docid: 152071
negative_passages.text: Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
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: 58014
negative_passages.text: Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.
negative_passages.docid: 1558
negative_passages.text: Number of homomorphisms between two cyclic groups.
negative_passages.docid: 62035
negative_passages.text: Order of automorphism group of cyclic group
negative_passages.docid: 145112
negative_passages.text: Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
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: 73248
negative_passages.text: Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group
negative_passages.docid: 122353
negative_passages.text: Status of the classification of non-finitely generated abelian groups.
negative_passages.docid: 73211
negative_passages.text: Cyclic subgroups dealing with prime numbers Question
negative_passages.docid: 147517
negative_passages.text: Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
negative_passages.docid: 98155
negative_passages.text: Free products of cyclic groups
negative_passages.docid: 76504
negative_passages.text: Non-trivial cyclic group with unique generator
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.