Group theory and generalizations Foundations Concept
Subgroup
Summary
A subgroup of a group is a subset that is itself a group under the same operation.
Where this leads
44 pages build on this one.
- Fractional factorial design
- Zassenhaus lemma
- Artin's induction theorem
- Closed subgroup theorem
- Lagrange's theorem in S3
- Open subgroup
- Automorphic form
- Artin reciprocity law
- Permutation group
- Induced representation
- Pariah groups
- Class field theory
- Quotient of a topological group
- Magnus's Freiheitssatz
- Arithmetic group
- Specht module
- Cartan's theorem on continuous homomorphisms
- Subnormal subgroup
- Hall subgroup
- Congruence subgroup
- Frattini subgroup
- Gelfand pair
- Stallings theorem about ends of groups
- Krohn–Rhodes theory
- Hilbert class field
- Lie subgroup
- Decomposition group
- Higman embedding theorem
- Frobenius reciprocity
- Schreier refinement theorem
- Discrete subgroup
- Tits alternative
- Gromov's theorem on groups of polynomial growth
- Kurosh subgroup theorem
- HNN extension
- No small subgroups
- Brauer's theorem on induced characters
- Transfer homomorphism
- Nielsen–Schreier theorem
- Schreier coset graph
- Matrix Lie group
- Ramification group
- Frobenius group
- Lattice (group)
Further reading
- Web https://en.wikipedia.org/wiki/Subgroup, lead section
About this page
| Tag | 0X1JXT47GA |
|---|---|
| URI | m2://0X1JXT47GA |
| Kind | concept |
| Writing | W2 usable |
| MSC | 20A05 |
| Specializes | Group |
| Same as |
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What this page needs for W3
- section Motivation: the question that the notion answers (0 of 1)
- section History: who introduced the notion and when (0 of 1)
- explanations for the audience (0 of 3)
- a person confirmed each agent-written section: rule P04 (0 of 1)
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What links here
Special cases
- Sylow p-subgroup
- Centraliser
- Stabiliser
- Normal subgroup
- Torsion subgroup
- Conjugate subgroup
- Subgroup generated by a subset
- Normaliser
- Congruence subgroup
- Discrete subgroup
- Ramification group
- Subnormal subgroup
- Hall subgroup
- Lie subgroup
- Open subgroup
- Permutation group
Definitions
Used by
- Fractional factorial design
- Zassenhaus lemma
- Artin's induction theorem
- Closed subgroup theorem
- Lagrange's theorem in S3
- Open subgroup
- Automorphic form
- Permutation group
- Induced representation
- Pariah groups
- Class field theory
- Quotient of a topological group
- Magnus's Freiheitssatz
- Arithmetic group
- Specht module
- Subnormal subgroup
- Hall subgroup
- Congruence subgroup
- Frattini subgroup
- Gelfand pair
- Stallings theorem about ends of groups
- Krohn–Rhodes theory
- Lie subgroup
- Decomposition group
- Higman embedding theorem
- Frobenius reciprocity
- Discrete subgroup
- Tits alternative
- Gromov's theorem on groups of polynomial growth
- Kurosh subgroup theorem
- HNN extension
- No small subgroups
- Brauer's theorem on induced characters
- Transfer homomorphism
- Nielsen–Schreier theorem
- Schreier coset graph
- Matrix Lie group
- Ramification group
- Frobenius group
- Lattice (group)