Frankl's Conjecture for subgroup lattices
Combinatorics
2020-07-08 v2 Group Theory
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.
Cite
@article{arxiv.1606.00011,
title = {Frankl's Conjecture for subgroup lattices},
author = {Alireza Abdollahi and Russ Woodroofe and Gjergji Zaimi},
journal= {arXiv preprint arXiv:1606.00011},
year = {2020}
}
Comments
8 pages; v2 fixes minor errors and adds reference on generation of Suzuki groups