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On Hering's flag transitive plane of order 27

Published online by Cambridge University Press:  17 April 2009

M.L. Narayana Rao ,
K. Kuppuswamy Rao  and
K. Satyanarayana
M.L. Narayana Rao
Affiliation:
Department of Mathematics, University College of Science, Osmania University, Hyderabad 500 007, India.
K. Kuppuswamy Rao
Affiliation:
Department of Mathematics, University College of Science, Osmania University, Hyderabad 500 007, India.
K. Satyanarayana
Affiliation:
Department of Mathematics, University College of Science, Osmania University, Hyderabad 500 007, India.
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Abstract

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The full collineation group of the flag transitive plane of order 27 constructed by Hering is determined. It is shown that the stabilizer of the origin of this plane is of order 2184.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 117 - 123
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]André, Jóhannes, “Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe”, Math. Z. 60 (1954), 156–186.Google Scholar
[2]Hering, Christoph, “Eine nicht-desarguessche zweifach transitive affine Ebene der Ordnung 27”, Abh. Math. Sem. Univ. Hamburg 34 (1970), 203–208.Google Scholar
[3]Pickert, Günter, Projecktive Ebenen (Die Grundlehren der mathematischen Wissenschaften, 80. Springer-Verlag, Berlin, Gottingen, Heidelberg, 1955).Google Scholar
[4]Rao, M.L. Narayana and Rao, K. Kuppuswamy, “A new flag transitive affine plane of order 27”, Proc. Amer. Math. Soc. 59 (1976), 337–345.CrossRefGoogle Scholar