Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A lattice in group theory is a partially ordered set of subgroups of a group, ordered by inclusion, in which every two elements have a unique supremum and infimum.
|
| gptkbp:example |
The set of all subgroups of a group forms a lattice under inclusion.
|
| gptkbp:field |
abstract algebra
group theory |
| https://www.w3.org/2000/01/rdf-schema#label |
lattice (group theory)
|
| gptkbp:property |
The meet of two subgroups is their intersection.
The join of two subgroups is the subgroup generated by their union. |
| gptkbp:relatedTo |
lattice (order theory)
subgroup lattice |
| gptkbp:seeAlso |
distributive lattice
modular lattice normal subgroup lattice |
| gptkbp:usedIn |
classification of finite groups
modular lattice theory study of normal subgroups |
| gptkbp:bfsParent |
gptkb:Margulis_arithmeticity_theorem
|
| gptkbp:bfsLayer |
5
|