Frobenius theorem (group theory)
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
gptkb:Frobenius_groups
finite groups |
| gptkbp:field |
group theory
|
| gptkbp:hasApplication |
representation theory
permutation groups |
| https://www.w3.org/2000/01/rdf-schema#label |
Frobenius theorem (group theory)
|
| gptkbp:implies |
existence of a normal complement
|
| gptkbp:namedAfter |
gptkb:Ferdinand_Georg_Frobenius
|
| gptkbp:publicationYear |
1895
|
| gptkbp:publishedIn |
gptkb:Sitzungsberichte_der_Königlich_Preußischen_Akademie_der_Wissenschaften_zu_Berlin
|
| gptkbp:relatedTo |
gptkb:Frobenius_complement
gptkb:Frobenius_kernel |
| gptkbp:state |
If a finite group G has a proper, nontrivial subgroup H such that H ∩ H^g = {1} for all g not in H, then G has a normal subgroup N such that G is the semidirect product of N and H.
|
| gptkbp:usedIn |
classification of finite groups
|
| gptkbp:bfsParent |
gptkb:Frobenius'_theorem
|
| gptkbp:bfsLayer |
7
|