Frankl's Conjecture for Subgroup Lattices

  • Alireza Abdollahi
  • Russ Woodroofe
  • Gjergji Zaimi
DOI: https://doi.org/10.37236/6248
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
How to Cite
Abdollahi, A., Woodroofe, R., & Zaimi, G. (2017). Frankl’s Conjecture for Subgroup Lattices. The Electronic Journal of Combinatorics, 24(3), P3.25. https://doi.org/10.37236/6248
Issue
Volume 24, Issue 3 (2017)
Article Number
P3.25