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, Volume 20, Issue 3, pp 223–228 | Cite as

Whaley's Theorem for Finite Lattices

  • Ralph Freese
  • Jennifer Hyndman
  • J. B. Nation
Article

Abstract

Whaley's Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/3. It is also shown that that every finite modular lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/2, and every finite distributive lattice L with |L|≥4 contains a proper sublattice S with |S|≥3/4|L|.

lattice ordered set sublattice maximal sublattice 

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References

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Ralph Freese
    • 1
  • Jennifer Hyndman
    • 1
  • J. B. Nation
    • 1
  1. 1.Department of MathematicsUniversity of HawaiiHonoluluU.S.A.

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