Zassenhaus neighborhood
E827067
The Zassenhaus neighborhood is a concept in group theory that describes a specific series of subgroups used to analyze the structure and composition factors of finite groups.
Statements (26)
| Predicate | Object |
|---|---|
| instanceOf |
group theory concept
ⓘ
mathematical concept ⓘ |
| appliesTo | finite groups ⓘ |
| concerns |
chains of subgroups
ⓘ
factor groups ⓘ |
| context |
abstract algebra
ⓘ
group extensions ⓘ |
| describes | a specific series of subgroups of a group ⓘ |
| field | group theory ⓘ |
| hasProperty |
captures local structure around a subgroup in a series
ⓘ
depends on a chosen series of subgroups ⓘ |
| hasPurpose |
to compare different subgroup series of a group
ⓘ
to control the composition factors arising from subgroup series ⓘ |
| namedAfter | Hans Zassenhaus NERFINISHED ⓘ |
| relatedTo |
Jordan–Hölder theorem
NERFINISHED
ⓘ
Zassenhaus lemma NERFINISHED ⓘ butterfly lemma NERFINISHED ⓘ chief series ⓘ composition series ⓘ refinement of subgroup series ⓘ subnormal series ⓘ |
| studiedIn | theory of finite solvable groups ⓘ |
| usedBy | group theorists ⓘ |
| usedFor |
analyzing the structure of finite groups
ⓘ
studying composition factors of finite groups ⓘ |
| usedIn | finite group theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.