Planar group

From Groupprops
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This group property arises from a property of lattices, viz the group property is satisfied only if the lattice of subgroups satisfies the corresponding property of lattices

Definition

A planar group is a group whose lattice of subgroups is planar.

Examples

See classification of finite planar groups.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Hasse planar group Lattice of subgroups can be embedded in a plane so that the y-coordinate of any maximal subgroup of a subgroup is less than the y-coordinate of the subgroup
finite planar group planar group that is finite

References