Group theory and generalizations Finite groups Concept
Nilpotent group
Summary
A nilpotent group is a group that has a central series of finite length. Equivalently, its lower central series reaches the trivial subgroup, or its upper central series reaches the whole group.
Where this leads
15 pages build on this one.
- Nilpotency class
- Oscillator representation
- Fitting subgroup
- Iwasawa manifold
- Frattini subgroup
- Nilmanifold
- Zassenhaus neighbourhood
- Margulis lemma
- Gromov's theorem on groups of polynomial growth
- Nilpotent Lie group
- Frobenius's theorem on Frobenius kernels
- Malcev completion
- Frobenius group
- Stone–von Neumann theorem
- Heisenberg group
Further reading
About this page
| Tag | 0Q7MMQHC1P |
|---|---|
| URI | m2://0Q7MMQHC1P |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20F18 |
| Specializes | Solvable 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
- Nilpotency class
- Fitting subgroup
- Frattini subgroup
- Zassenhaus neighbourhood
- Margulis lemma
- Gromov's theorem on groups of polynomial growth
- Nilpotent Lie group
- Frobenius's theorem on Frobenius kernels
- Malcev completion
- Heisenberg group