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A New Class of Translation Planes Constructed by Hyper-regulus Replacement

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Abstract.

A new class of translation planes of order qn that admit very small affine homology groups is constructed. These planes are constructed by the replacement of a new hyper-regulus that cannot be an André hyper-regulus. Hence, the planes cannot be André or generalized André.

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Authors and Affiliations

  1. Mathematics Department, Caledonian University, Cowcaddens Road, Glasgow, Scotland

    Vikram Jha

  2. Mathematics Department, University of Iowa, Iowa City, Iowa, 52242, USA

    Norman L. Johnson

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  1. Vikram Jha
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  2. Norman L. Johnson
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Correspondence to Vikram Jha.

Additional information

The ideas for this work originated when the second author was visiting Caledonian University under a grant from the London Mathematical Society in May of 2004. The authors are grateful to the University and to the LMS for their support for this work.

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Jha, V., Johnson, N.L. A New Class of Translation Planes Constructed by Hyper-regulus Replacement. J. geom. 90, 83–99 (2008). https://doi.org/10.1007/s00022-008-1976-5

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  • DOI: https://doi.org/10.1007/s00022-008-1976-5

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