Dimension and automorphism groups of lattices
Tóm tắt
Every group is the automorphism group of a lattice of order dimension at most 4. We conjecture that the automorphism groups of finite modular lattices of bounded dimension do not represent every finite group. It is shown that ifp is a large prime dividing the order of the automorphism group of a finite modular latticeL then eitherL has high order dimension orM
p, the lattice of height 2 and orderp+2, has a cover-preserving embedding inL. We mention a number of open problems.
Tài liệu tham khảo
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