query: Quotient group G/Z is cyclic
positive_passages.docid: 23394
positive_passages.text: If $G/Z(G)$ is cyclic, then $G$ is abelian
negative_passages.docid: 38853
negative_passages.text: Cyclic group of prime order
negative_passages.docid: 8623
negative_passages.text: Finite subgroups of the multiplicative group of a field are 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: 151025
negative_passages.text: If G is a group of order n=35, then it is cyclic
negative_passages.docid: 17077
negative_passages.text: Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.
negative_passages.docid: 70298
negative_passages.text: Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
negative_passages.docid: 1558
negative_passages.text: Number of homomorphisms between two cyclic groups.
negative_passages.docid: 152954
negative_passages.text: Extensions of finite cyclic groups
negative_passages.docid: 57887
negative_passages.text: When are the product of cyclic groups also cyclic?
negative_passages.docid: 25748
negative_passages.text: If $G / Z(G)$ nilpotent then G is nilpotent.
negative_passages.docid: 3907
negative_passages.text: Abelian quotient group
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: 144258
negative_passages.text: How to show a group 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: 13734
negative_passages.text: Show that every group of prime order is cyclic