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


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).

DOI Code: 10.1285/i15900932v24n2p59

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

Classification: 51E23; 51A40

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