query: Why can't G/Z(G) be nontrivial and cyclic?
positive_passages.docid: 23394
positive_passages.text: If $G/Z(G)$ is cyclic, then $G$ is abelian
negative_passages.docid: 135524
negative_passages.text: Is $\mathrm{ZFC}^E$ outright inconsistent?
negative_passages.docid: 75254
negative_passages.text: Properties possessed by $H , G/H$ but not G
negative_passages.docid: 117178
negative_passages.text: Cyclic group generators
negative_passages.docid: 76446
negative_passages.text: Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
negative_passages.docid: 57887
negative_passages.text: When are the product of cyclic groups also cyclic?
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 32362
negative_passages.text: Detail in bijection between Inn(G) and G/Z(G)?
negative_passages.docid: 92430
negative_passages.text: Show that the group is cyclic.
negative_passages.docid: 53335
negative_passages.text: Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
negative_passages.docid: 43155
negative_passages.text: Cyclotomic Polynomials and GCD
negative_passages.docid: 151354
negative_passages.text: Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
negative_passages.docid: 25744
negative_passages.text: Multiplication in Permutation Groups Written in Cyclic Notation
negative_passages.docid: 63691
negative_passages.text: G acts on X transitively, then there exists some element that does not have any fixed points
negative_passages.docid: 28452
negative_passages.text: Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
negative_passages.docid: 77297
negative_passages.text: Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$