Locally cyclic group
Summary
A group is locally cyclic if every finitely generated subgroup is cyclic. Every cyclic group is locally cyclic, and every finitely-generated locally cyclic group is cyclic. Every locally cyclic group is abelian. Every subgroup, every quotient group and every homomorphic image of a locally cyclic group is locally cyclic.
Further reading
- Wikipedia, page 249268, revision 1353640923, Glossary of group theory, section L. adopted
About this page
| Tag | RXWA8TF2RM |
|---|---|
| URI | m2://RXWA8TF2RM |
| Kind | concept |
| Writing | W1 stated |
| Changed | 3 November 2026 |
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- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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