Planar group
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 -coordinate of any maximal subgroup of a subgroup is less than the -coordinate of the subgroup | |||
| finite planar group | planar group that is finite |
References
- Planar Infinite Groups (fix this ref up later)