Finite groups with planar subgroup lattices

Abstract

It is natural to ask when a group has a planar Hasse lattice or more generally when its subgroup graph is planar. In this paper, we completely answer this question for finite groups. We analyze abelian groups, p-groups, solvable groups, and nonsolvable groups in turn. We find seven infinite families (four depending on two parameters, one on three, two on four), and three "sporadic" groups. In particular, we show that no nonabelian group whose order has three distinct prime factors can be planar.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1007/s10801-006-7392-8

Keywords

Graph, Lattice-planar, Nonabelian group, Planar, Subgroup graph

Publication Date

5-1-2006

Journal Title

Journal of Algebraic Combinatorics

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