Every Finite Group is the Automorphism Group of Some Finite Orthomodular Lattice
Copyright policy )Every Finite Group is the Automorphism Group of Some Finite Orthomodular Lattice
If L L is a lattice, the automorphism group of L L is denoted Aut ( L ) \operatorname {Aut} (L) . It is known that given a finite abstract group H H , there exists a finite distributive lattice D D such that Aut ( D ) ≅ H \operatorname {Aut} (D) \cong H . It is also known that one cannot expect to find a finite orthocomplemented distributive (Boolean) lattice B B such that Aut ( B ) ≅ H \operatorname {Aut} (B) \cong H . In this paper it is shown that there does exist a finite orthomodular lattice L L such that Aut ( L ) ≅ H \operatorname {Aut} (L) \cong H .
Complemented lattices, orthocomplemented lattices and posets, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Structure theory of Boolean algebras, Logical aspects of Boolean algebras, Combinatorial aspects of finite geometries, Graphs and abstract algebra (groups, rings, fields, etc.)
Complemented lattices, orthocomplemented lattices and posets, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Structure theory of Boolean algebras, Logical aspects of Boolean algebras, Combinatorial aspects of finite geometries, Graphs and abstract algebra (groups, rings, fields, etc.)
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