Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-01T01:41:27.161Z Has data issue: false hasContentIssue false

Finite groups as automorphism groups of orthocomplemented projective planes

Published online by Cambridge University Press:  09 April 2009

Richard J. Greechie
Affiliation:
Department of Mathematics Kansas State UniversityManhattan Kansas 66506, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A construction is given for a non-desarguesian projective plane P and an absolute-point free polarity on P such that the group of collineations of P which commute with the polarity is isomorphic to an arbitrary preassigned finite group.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

Frucht, R. (1949), “Graphs of degree three with a given abstract group”, Canad. J. Math. 1, 365378.CrossRefGoogle Scholar
Greechie, R. J. (1974), “Some results from the combinatorial approach to quantum logic”, Synthese 29, 113127.CrossRefGoogle Scholar
Schrag, G. C. (1971), “Combinatorics and graph techniques in orthomodular theory”, Ph.D. Dissertation, Kansas State University.Google Scholar
Schrag, G. C. (1976), “Every finite group is the automorphism group of some finite orthomodular lattice”, PAMS, 55 (1), 243249.CrossRefGoogle Scholar
Sabidussi, G. (1957), “Graphs with given group and given graph-theoretical properties”, Canad. J. Math. 9, 515517.CrossRefGoogle Scholar