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Automorphism groups of orthomodular lattices

Published online by Cambridge University Press:  17 April 2009

Gudrun Kalmbach
Gudrun Kalmbach
Affiliation:
Abt. Math. III. O.E., Universitat Ulm, D-7900 Ulm, Federal Republic of Germany and Department of Mathematics, Institute of Advanced Studies, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
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Abstract

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Every group is the automorphism group of an orthomodular lattice.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 309 - 313
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Birkhoff, G., Lattice theory, 3rd edition (American Mathematical Society Colloquium Publications, 25. American Mathematical Society, Providence, Rhode Island, 1973).Google Scholar
[2]Greechie, R., “Finite groups as automorphism groups of ortho-complemented projective planes”, J. Austral. Math. Soc. 25 (1978), 19–24.CrossRefGoogle Scholar
[3]Gudder, S., “Representations of groups as automorphisms on orthomodular lattices and posets”, Canad. J. Math. 23 (1971), 659–673.CrossRefGoogle Scholar
[4]Jónsson, B., Topics in universal algebra (Lecture Notes in Mathematics, 250. Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
[5]Kalmbach, G., Orthomodular lattices (Academic Press, London, 1983).Google Scholar
[6]Kalmbach, G., “Orthomodular lattices do not satisfy any special lattice equation”, Arch. Math. (Basel) 28 (1977), 7–8.CrossRefGoogle Scholar
[7]McKenzie, R. and Monk, J., “On automorphism groups of Boolean algebras”, Infinite and finite sets, 951–988 (Colloq. Math. Soc. J. Bolyai, 10. North-Holland, Amsterdam, 1973).Google Scholar
[8]Morash, R., “Angle bisection and orthoautomorphisms in Hilbert lattices”, Canad. J. Math. 25 (1973), 261–272.CrossRefGoogle Scholar
[9]Rosenstein, J., Linear orderings (Academic Press, New York, 1982).Google Scholar
[10]Sabidussi, G., “Graphs with given group and given graph-theoretical properties”, Canad. J. Math. 9 (1957), 515–525.CrossRefGoogle Scholar
[11]Schrag, G., “Every finite group is the automorphism group of some finite orthomodular lattice”, Proc. Amer. Math. Soc. 55 (1976), 243–249.CrossRefGoogle Scholar