Frankl's Conjecture for Subgroup Lattices
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.