Orbit constructions for translation planes of order 81 admitting SL(2,5)


The authors have classified all translation planes of order 81 that admit SL(2,5), where the 3-elements are elations, with the use of the computer. In this article, it is shown that the spreads in PG(3,9) may be obtained directly from the group SL(2,5). In the process, there is a construction of a replaceable 12-nest of reguli of a Desarguesian plane.

DOI Code: 10.1285/i15900932v24n2p41

Keywords: Spread; $SL(2,5)$ elation group; Baer group

Classification: 51E23; 51A40

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