Thetranslation planes of order 81 admitting ![SL(2,5)](https://358864.dpsou.asia/plugins/generic/latexRender/cache/6bdc7b8e6abd35a3793c8fc9a4425be7.png)
Abstract
Johnson and Prince have classified all translation planes of order 81 that admit
, where the 3-elements are elations. In this article, it is shown that whenever
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
; there are exactly 14 translation planes of order 81 admitting
.
![SL(2,5)](https://358864.dpsou.asia/plugins/generic/latexRender/cache/6bdc7b8e6abd35a3793c8fc9a4425be7.png)
![SL(2,5)](https://358864.dpsou.asia/plugins/generic/latexRender/cache/6bdc7b8e6abd35a3793c8fc9a4425be7.png)
![SL(2,5)](https://358864.dpsou.asia/plugins/generic/latexRender/cache/6bdc7b8e6abd35a3793c8fc9a4425be7.png)
![SL(2,5)](https://358864.dpsou.asia/plugins/generic/latexRender/cache/6bdc7b8e6abd35a3793c8fc9a4425be7.png)
DOI Code:
10.1285/i15900932v24n2p59
Keywords:
Spread; $SL(2,5)$ elation group; Baer group
Classification:
51E23; 51A40
Full Text: PDF