TY - JOUR

T1 - On the representation of lattices by subgroup lattices

AU - Repnitskii, V. B.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Whitman's condition in a lattice L means that, for any elements a, b, c, d ∈ L, a ∧ b ≤ c ∨ d implies either a ∧ b ≤ c or a ∧ b ≤ d, or a ≤ c ∨ d, or b ≤ c ∨ d. We prove that any lattice satisfying Whitman's condition can be embedded in the subgroup lattice of a free group of an arbitrary non-soluble group variety. Some interesting corollaries (both on embeddings in lattices of subgroups and others) are examined.

AB - Whitman's condition in a lattice L means that, for any elements a, b, c, d ∈ L, a ∧ b ≤ c ∨ d implies either a ∧ b ≤ c or a ∧ b ≤ d, or a ≤ c ∨ d, or b ≤ c ∨ d. We prove that any lattice satisfying Whitman's condition can be embedded in the subgroup lattice of a free group of an arbitrary non-soluble group variety. Some interesting corollaries (both on embeddings in lattices of subgroups and others) are examined.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=0039176401

U2 - 10.1007/PL00000330

DO - 10.1007/PL00000330

M3 - Article

VL - 37

SP - 81

EP - 105

JO - Algebra Universalis

JF - Algebra Universalis

SN - 0002-5240

IS - 1

ER -