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A translation plane of order 81 and its full collineation group

Published online by Cambridge University Press:  17 April 2009

Vito Abatangelo
Vito Abatangelo
Affiliation:
Dipartimento di Matematica, Via Re David 200, 70125 Bari, Italy.
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Abstract

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In this paper a new translation plane of order 81 is constructed. Its collineation group is solvable and acts on the line at infinity as a permutation group K which is the product of a group of order 5 belonging to the center of K with a group of order 48. A 2-Sylow subgroup of K is the direct product of a dihedral group of order 8 with a group of order 2. K admits six orbits. They have lengths 4, 6, 12, 12, 24, 24.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1984 , pp. 19 - 34
Copyright
Copyright © Australian Mathematical Society 1984

References

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