Frankl's Conjecture for Subgroup Lattices

  • Alireza Abdollahi
  • Russ Woodroofe
  • Gjergji Zaimi
Keywords: Extremal combinatorics, Subgroup lattice, Finite simple groups

Abstract

We show that the subgroup lattice of any finite group satisfies Frankl’s Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common technical result used to prove both may be of some independent interest.

Published
2017-08-11
Article Number
P3.25