query: Simple example of an non-cyclic group
positive_passages.docid: 147366
positive_passages.text: What are a few examples of noncyclic finite groups?
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: 90256
negative_passages.text: Example of a simple graph isomorphic to a permutation group.
negative_passages.docid: 147158
negative_passages.text: Galois group of a non-separable polynomial
negative_passages.docid: 18182
negative_passages.text: An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
negative_passages.docid: 117815
negative_passages.text: Non-abelian group $G$ satisfying $(a \cdot b)^i=a^i \cdot b^i,$ for two consecutive integers.
negative_passages.docid: 32127
negative_passages.text: Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective
negative_passages.docid: 129830
negative_passages.text: A group with no proper non-trivial subgroups
negative_passages.docid: 58688
negative_passages.text: Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
negative_passages.docid: 127030
negative_passages.text: Simple example of non-arithmetic ring (non-distributive ideal lattice)
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: 160
negative_passages.text: homeomorphism non-example
negative_passages.docid: 71035
negative_passages.text: Non abelian subgroup of a abelian group.
negative_passages.docid: 112263
negative_passages.text: an example for $\pi$-quasinormal subgroup but is not normal
negative_passages.docid: 11541
negative_passages.text: Examples of a non-commutative division ring
negative_passages.docid: 112933
negative_passages.text: Show that $Z\times Z$ is not cyclic...