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A class of translation planes of square order

Published online by Cambridge University Press:  17 April 2009

M.L. Narayana Rao ,
K. Satyanarayana  and
G. Vithal Rao
M.L. Narayana Rao
Affiliation:
Department of Mathematics, Osmania University, Hyderabad–500 007, India
K. Satyanarayana
Affiliation:
Department of Mathematics, Osmania University, Hyderabad–500 007, India
G. Vithal Rao
Affiliation:
Department of Mathematics, Osmania University, Hyderabad–500 007, India
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Abstract

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A class of translation planes of order p2r, where r is an odd natural number and p is a prime, p ≥ 7, p ≢ ± (mod 10) is constructed. A salient feature shared by all these planes is that one ideal point is fixed by the translation complement and the remaining ideal points are divided into at least two orbits, one of which is of length pr.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 1 , August 1984 , pp. 59 - 66
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Dembowski, P., Finite Geometries (Springer-Verlag, Berlin, 1968).Google Scholar
[2]Foulser, D.A., “A generalization of André's systems”, Math. Z. 100 (1967), 380–395.CrossRefGoogle Scholar
[3]Hering, C., “A new class of quasifields”, Math. Z. 118 (1970), 56–57.CrossRefGoogle Scholar
[4]Maduram, D.M., “Matrix representation of translation planes”, Geom. Dedicata, 4 (1975), 485–492.CrossRefGoogle Scholar
[5]Rao, M.L. Narayana, “A class of flag transitive planes”, Proc. Amer. Math. Soc., 39 (1973), 51–56.CrossRefGoogle Scholar
[6]Rao, M.L. Narayana and Satyanarayana, K., “A new class of square order planes”, J. Combin. Theory Ser. A, 35 (1983), 33–42.Google Scholar
[7]Satyanarayana, K., “On some translation planes of square and cube orders and their translation complements”, (PhD Dissertation, Osmania University, India, 1982).Google Scholar
[8]Walker, M., “A class of translation planes”, Geom. Dedicata 5 (1976), 135–146.CrossRefGoogle Scholar