Group theory and generalizations Foundations Concept
Order of an element
Summary
The order of an element of a group is the smallest positive integer such that the th power of the element is the identity. When no such exists, the element has infinite order.
Where this leads
13 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Order_(group_theory), lead section
About this page
| Tag | 0WE2NHZJ7B |
|---|---|
| URI | m2://0WE2NHZJ7B |
| Aliases | period-of-an-element |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20A05 |
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What this page needs for W2
- 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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Definitions
Used by
- Z* theorem
- Elementary abelian group
- Brauer character
- Nagell–Lutz theorem
- Period and index
- Brauer–Fowler theorem
- Torsion group
- Torsion-free group
- Burnside problem