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A translation plane of order 25 and its full collineation group

Published online by Cambridge University Press:  17 April 2009

M.L. Narayana Rao  and
K. Kuppuswamy Rao
M.L. Narayana Rao
Affiliation:
Department of Mathematics, Osmania University, Hyderabad, Andhra Pradesh, India.
K. Kuppuswamy Rao
Affiliation:
Department of Mathematics, Osmania University, Hyderabad, Andhra Pradesh, India.
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Abstract

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Ostrom proposed classifications of translation planes on the basis of the action of the collineation group of the plane on the ideal points. There are examples of translation planes in which ideal points form a single orbit (flag transitive planes) and also several orbits (Hall, André, Foulser, and so forth, planes). In this paper the authors have constructed a translation plane in which the ideal points are divided into two orbits of lengths 18 and 8 respectively. A few collineatlons are computed together with their actions. The group of collineations G1 which is transitive on the two sets of 18 and 8 lines separately is calculated. All the collineations that fix L0 are also calculated and they form a group of. If G2 is the group of translations then the full collineation group is shown to be 〈G1, G2, G3〉.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 351 - 362
Copyright
Copyright © Australian Mathematical Society 1979

References

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