Thetranslation planes of order 81 admitting $SL(2,5)$

Authors

  • Vikram Jha
  • Norman L. Johnson

DOI:

https://doi.org/10.1285/i15900932v24n2p59

Keywords:

Spread, $SL(2, 5)$ elation group, Baer group

Abstract

Johnson and Prince have classified all translation planes of order 81 that admit $SL(2,5)$, where the 3-elements are elations. In this article, it is shown that whenever $SL(2,5)$ acts as a collineation group on a translation plane of order 81, the problem can always be reduced to the elation case. Hence, there is a complete classification of all translation planes of order 81 admitting $SL(2,5)$; there are exactly 14 translation planes of order 81 admitting $SL(2,5)$.

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Published

25-10-2005

Issue

Volume 24, Issues 2 (2005)

Section

Articoli

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode