Group theory and generalizations Foundations Concept
Quotient group
Summary
The quotient group of a group by a normal subgroup is the set of cosets of , with the product . It collapses to the identity and keeps the rest of the structure of .
Where this leads
29 pages build on this one.
- Zassenhaus lemma
- Horocycle flow
- Z* theorem
- Weyl group of a compact Lie group
- Profinite completion
- Maass wave form
- Modular curve
- Idele class group
- Geodesic flow on a locally symmetric space
- Supersolvable group
- Pariah groups
- Quotient of a topological group
- Selberg's 1/4 conjecture
- Extraspecial group
- Ideal class group
- Congruence subgroup
- j-invariant
- Modular form
- Galois correspondence for coverings
- Chevalley's structure theorem
- Petersson inner product
- Schreier refinement theorem
- Hopf's formula
- Cusp form
- Fundamental domain of the modular group
- Topological modular forms
- Lyndon–Hochschild–Serre spectral sequence
- Modular group
- Complex torus
Further reading
- Web https://en.wikipedia.org/wiki/Quotient_group, Definition
About this page
| Tag | 0KYX2N69J0 |
|---|---|
| URI | m2://0KYX2N69J0 |
| Aliases | factor-group |
| Kind | concept |
| Writing | W2 usable |
| MSC | 20A05 |
| Specializes | Group |
| Same as |
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Used by
- Zassenhaus lemma
- Z* theorem
- Weyl group of a compact Lie group
- Profinite completion
- Idele class group
- Supersolvable group
- Pariah groups
- Quotient of a topological group
- Extraspecial group
- Ideal class group
- Galois correspondence for coverings
- Chevalley's structure theorem
- Schreier refinement theorem
- Hopf's formula
- Lyndon–Hochschild–Serre spectral sequence
- Modular group
- Complex torus