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Translation planes of order q 2 admitting a two-transitive orbit of length q + 1 on the line at infinity

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Abstract

A classification is given of all translation planes of order q 2 that admit a collineation group G admitting a two-transitive orbit of q + 1 points on the line at infinity.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Lecce, Via Arnesano, 73100, Lecce, Italy

    M. Biliotti & A. Montinaro

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

    V. Jha

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

    N. L. Johnson

Authors
  1. M. Biliotti
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  2. V. Jha
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  3. N. L. Johnson
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  4. A. Montinaro
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Corresponding author

Correspondence to N. L. Johnson.

Additional information

It has been said by many mathematicians that they became interested in finite geometry due to the absolutely magnetic excitement generated for this subject by Dan Hughes. In the early days of the area of finite geometry, Dan’s contributions to the subject came from almost every conceivable direction –from the amazing ‘Hughes Planes’, his tremendous insights in the construction technique of ‘derivation’, new directions in group actions on finite incidence structures, to his beautiful constructions of semifield planes. Dan’s influence seemed to be everywhere and of course, there is more: free geometries, his fundamental work on ‘t-designs’ and inversive planes as well as generalized quadrangles and partital geometries. Certainly, the ‘Hughes-Piper’ school at Westfield College of the University of London was and is extraordinarily influential as their many strong students continue in this tradition of excellence. Each of the authors were influenced by Dan’s work, either directly or indirectly, and his original passion for this subject is mirrored in the explosive growth of this subject over the last 50 years, and Dan, we could not have done it without you. Therefore, in recognition of his extraordinary life and career, the authors would like to dedicate this article to our great friend Dan Hughes in celebration of his 80th birthday.

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Biliotti, M., Jha, V., Johnson, N.L. et al. Translation planes of order q 2 admitting a two-transitive orbit of length q + 1 on the line at infinity. Des. Codes Cryptogr. 44, 69–86 (2007). https://doi.org/10.1007/s10623-007-9063-8

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  • DOI: https://doi.org/10.1007/s10623-007-9063-8

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