Group theory and generalizations Foundations Concept
Cyclic group
Summary
A cyclic group is a group that one element generates. Up to isomorphism, the cyclic groups are the integers and the integers modulo under addition.
Where this leads
12 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Cyclic_group, Definition and notation
About this page
| Tag | 0KVGH0J5B3 |
|---|---|
| URI | m2://0KVGH0J5B3 |
| Aliases | monogenous-group |
| Kind | concept |
| Writing | W2 usable |
| MSC | 20A05 |
| Specializes | Abelian group |
| Same as |
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Used by
- Artin's induction theorem
- Sporadic group
- Kummer theory
- Supersolvable group
- Tate cohomology
- Primitive permutation group
- Cohomological dimension of a group
- Z-group
- Polycyclic group
- Mazur's torsion theorem
- Brauer's theorem on induced characters
- List of small groups