Group theory and generalizations Infinite groups and combinatorial group theory Concept
Free abelian group
Summary
A free abelian group is an abelian group with a basis. Each element is an integer combination of finitely many basis elements in exactly one way. The free abelian group of finite rank is isomorphic to .
Where this leads
17 pages build on this one.
- Dirichlet's unit theorem
- Minkowski bound
- Regulator of a number field
- Class number formula
- Class number
- Right-angled Artin group
- Abelian category
- Kronecker–Weber theorem
- Rank of an abelian group
- Whitehead problem
- Finiteness of the class number
- Hermite–Minkowski theorem
- Simplicial homology
- Dedekind zeta function
- Hilbert's eighteenth problem
- Singular homology
- Bieberbach theorems
Further reading
- Web https://en.wikipedia.org/wiki/Free_abelian_group, lead section
About this page
| Tag | 0WJX8MGG37 |
|---|---|
| URI | m2://0WJX8MGG37 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20K15, 20K20 |
| Specializes | Abelian group |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Dirichlet's unit theorem
- Right-angled Artin group
- Abelian category
- Rank of an abelian group
- Whitehead problem
- Simplicial homology
- Singular homology
- Bieberbach theorems