Frankl's Conjecture for Subgroup Lattices

Alireza Abdollahi, Russ Woodroofe, Gjergji Zaimi

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.


Keywords


Extremal combinatorics; Subgroup lattice; Finite simple groups

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