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

Schrag, Gerald

doi:10.1090/S0002-9939-1976-0398933-4

Every finite group is the automorphism group of some finite orthomodular lattice
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Proc. Amer. Math. Soc. 55 (1976), 243-249 Request permission

Abstract:

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 $\operatorname {Aut} (L) \cong H$.

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Additional Information

Journal: Proc. Amer. Math. Soc. 55 (1976), 243-249
DOI: https://doi.org/10.1090/S0002-9939-1976-0398933-4
MathSciNet review: 0398933