Group theory and generalizations Foundations Concept
Finitely generated group
Summary
A finitely generated group is a group that a finite subset generates. All finite groups and the group of integers are finitely generated.
Where this leads
19 pages build on this one.
- Conjugacy problem
- Word metric
- Kurosh problem
- Mordell's theorem
- Hyperbolic group
- Restricted Burnside problem
- Stallings theorem about ends of groups
- Polycyclic group
- Growth rate of a group
- Finitely presented group
- Congruent number problem
- Mordell–Weil theorem
- Švarc–Milnor lemma
- Higman embedding theorem
- Tits alternative
- Gromov's theorem on groups of polynomial growth
- Burnside problem
- Grushko theorem
- Birch and Swinnerton-Dyer conjecture
Further reading
About this page
| Tag | 082DWWXMRJ |
|---|---|
| URI | m2://082DWWXMRJ |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20F05 |
| Specializes | 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
Results about this
- Conjugacy problem
- Stallings theorem about ends of groups
- Švarc–Milnor lemma
- Higman embedding theorem
- Burnside problem
- Grushko theorem
Used by
- Conjugacy problem
- Word metric
- Mordell's theorem
- Hyperbolic group
- Restricted Burnside problem
- Stallings theorem about ends of groups
- Polycyclic group
- Growth rate of a group
- Finitely presented group
- Mordell–Weil theorem
- Švarc–Milnor lemma
- Higman embedding theorem
- Tits alternative
- Gromov's theorem on groups of polynomial growth
- Burnside problem
- Grushko theorem