Frankl's Conjecture for subgroup lattices

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.

arXiv comment8 pages; v2 fixes minor errors and adds reference on generation of Suzuki groups