Zassenhaus lemma
E827064
The Zassenhaus lemma is a fundamental result in group theory that describes how subgroups in a group extension correspond and relate to each other, often used in the study of composition series and the Jordan–Hölder theorem.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Zassenhaus lemma in group theory | 1 |
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
group theory lemma
ⓘ
mathematical theorem ⓘ |
| alsoKnownAs | butterfly lemma NERFINISHED ⓘ |
| appearsIn |
algebra textbooks
ⓘ
group theory monographs ⓘ |
| appliesTo |
groups
ⓘ
subgroups ⓘ |
| category |
theorems about finite groups
ⓘ
theorems about series of subgroups ⓘ |
| concerns |
correspondence between certain factor groups
ⓘ
isomorphisms between quotient groups ⓘ |
| describes | relations between subgroups in a group extension ⓘ |
| field | group theory ⓘ |
| hasDiagrammaticNickname | butterfly diagram ⓘ |
| hasGeneralization | results on modular lattices of subgroups ⓘ |
| hasRole | technical tool in the proof of Jordan–Hölder theorem ⓘ |
| implies | existence of isomorphisms between certain factor groups in two subgroup series ⓘ |
| namedAfter | Hans Zassenhaus NERFINISHED ⓘ |
| relatedTo |
Jordan–Hölder theorem
NERFINISHED
ⓘ
Schreier refinement theorem NERFINISHED ⓘ isomorphism theorems for groups NERFINISHED ⓘ |
| relatesConcept |
group extensions
ⓘ
normal subgroups ⓘ refinements of series of subgroups ⓘ subgroup lattices ⓘ |
| statedInTermsOf |
intersections of subgroups
ⓘ
products of subgroups ⓘ |
| typicalContext |
development of the Jordan–Hölder theorem
ⓘ
discussion of composition series and chief series ⓘ |
| usedFor |
comparing different subnormal series
ⓘ
refining series of subgroups ⓘ |
| usedIn |
proofs of the Jordan–Hölder theorem
ⓘ
study of composition series ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Zassenhaus lemma in group theory