Johnson, N. L. The maximal special linear groups which act on translation planes. (English) Zbl 0602.51003 Boll. Unione Mat. Ital., VI. Ser., A 5, 349-352 (1986). The author studies translation planes \(\pi\) of order \(q^ t\) admitting a collineation group G isomorphic to \(SL(2,p^ r)\) in the translation complement. By a result of D. A. Foulser and the author [J. Algebra 86, 385-406 (1984; Zbl 0527.51012), J. Geom. 18, 122-139 (1982; Zbl 0527.51013)] \(\pi\) is Desarguesian, Hall, Hering, Ott-Schaeffer, the Dempwolff plane of order 16, or one of the two Walker planes of order 25, if \(r=t\) or \(2r=t\). By counting the fixed components of elements whose order is a p-primitive prime divisor of \(p^{2r}-1,\) the author shows that there are no planes for \(t/2<r<t.\) Reviewer: G.Stroth Cited in 3 Documents MSC: 51A40 Translation planes and spreads in linear incidence geometry Keywords:translation planes Citations:Zbl 0527.51012; Zbl 0527.51013 PDFBibTeX XMLCite \textit{N. L. Johnson}, Boll. Unione Mat. Ital., VI. Ser., A 5, 349--352 (1986; Zbl 0602.51003)