Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
group theory concept
|
| gptkbp:application |
gptkb:Galois_theory
representation theory permutation groups |
| gptkbp:category |
gptkb:algebra
gptkb:mathematics |
| gptkbp:definedIn |
a finite group G with a proper nontrivial subgroup H such that H ∩ H^g = {1} for all g not in H
|
| gptkbp:example |
affine group over finite field
dihedral group of order 2n (n odd) |
| gptkbp:firstDescribed |
1895
|
| gptkbp:hasNormalSubgroup |
gptkb:Frobenius_kernel
|
| gptkbp:hasProperty |
gptkb:Frobenius_kernel
nontrivial proper subgroup (Frobenius complement) non-regular transitive permutation group |
| gptkbp:hasSubgroup |
gptkb:Frobenius_complement
|
| https://www.w3.org/2000/01/rdf-schema#label |
Frobenius groups
|
| gptkbp:isA |
gptkb:group_of_people
|
| gptkbp:namedAfter |
gptkb:Ferdinand_Georg_Frobenius
|
| gptkbp:order |
|G| = |K| × |H|, where K is the kernel and H is the complement
|
| gptkbp:studiedIn |
group theory
|
| gptkbp:theory |
gptkb:Frobenius_theorem
|
| gptkbp:bfsParent |
gptkb:Frobenius_theorem_(group_theory)
|
| gptkbp:bfsLayer |
8
|