Every finite group is the automorphism group of some finite orthomodular lattice

Abstract

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 .