Every Finite Group is the Automorphism Group of Some Finite Orthomodular Lattice
Gerald Schrag · Proceedings of the American Mathematical Society · 1976
If $L$ is a lattice, the automorphism group of $L$ is denoted $\operatorname {Aut} (L)$. It is known that given a finite abstract group $H$, there exists a finite distributive lattice $D$ such that $\operatorname {Aut} (D) \cong H$. It is also known that one cannot expect to find a finite orthocomplemented distributive (Boolean) lattice $B$ such that $\operatorname {Aut} (B) \cong H$. In this paper it is shown that there does exist a finite orthomodular lattice $L$ such that $\operatorname {Aut} (L) \cong H$.