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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


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

DOI: https://doi.org/10.1090/S0002-9939-1976-0398933-4
Keywords: Orthomodular lattices, automorphism groups, distributive lattices, graph theoretic methods, orthocomplemented lattices, Boolean lattices, graphs, finite incidence structures, orthogonality spaces, dual structures
Article copyright: © Copyright 1976 American Mathematical Society