Group theory and generalizations Foundations Concept
Index of a subgroup
Summary
The index of a subgroup in a group is the number of left cosets of in . For finite groups, it is .
Where this leads
23 pages build on this one.
- Profinite completion
- Schreier–Sims algorithm
- Schur–Zassenhaus theorem
- Nichols–Zoeller theorem
- Hall's theorem on solvable groups
- Induced representation
- Margulis normal subgroup theorem
- Arithmetic group
- Residually finite group
- Open subgroups are closed
- Hall subgroup
- Congruence subgroup
- Margulis arithmeticity theorem
- Sylow theorems
- Restricted Burnside problem
- Margulis lemma
- Tits alternative
- Gromov's theorem on groups of polynomial growth
- Hilbert's eighteenth problem
- Transfer homomorphism
- Nielsen–Schreier theorem
- Jordan–Schur theorem
- Bieberbach theorems
Further reading
- Web https://en.wikipedia.org/wiki/Index_of_a_subgroup, lead section
About this page
| Tag | 0DTXBQPA2S |
|---|---|
| URI | m2://0DTXBQPA2S |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20A05 |
| Same as |
Markdown · JSON · Edit on GitHub
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)
- edge specializes both: the more general notions and the special cases (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
Used by
- Profinite completion
- Schreier–Sims algorithm
- Schur–Zassenhaus theorem
- Nichols–Zoeller theorem
- Induced representation
- Margulis normal subgroup theorem
- Arithmetic group
- Residually finite group
- Open subgroups are closed
- Hall subgroup
- Congruence subgroup
- Margulis arithmeticity theorem
- Sylow theorems
- Restricted Burnside problem
- Margulis lemma
- Tits alternative
- Gromov's theorem on groups of polynomial growth
- Transfer homomorphism
- Nielsen–Schreier theorem
- Jordan–Schur theorem
- Bieberbach theorems