Geodesic
Remark to a Theorem Due to R. Sandler
Canadian journal of mathematics, Tome 22 (1970) no. 3, p. 518

Voir la notice de l'article provenant de la source Cambridge University Press

To prove [2, Theorem 1], it is enough to remark that if x is a point or line of F4 which is fixed under H, then x is fixed under each subgroup of H. By Sylow's theorem, H has a subgroup H’ of order three. By [1, p. 420, Lemma 2.2], it follows that x is in the subplane of F4 generated by those elements of {A, B, C, D} which are fixed under H'. This subplane consists of a point only. Hence, x is in {A, B, C, D}, which is impossible. This argument can be used in many other cases. 
Iden, Oddvar. Remark to a Theorem Due to R. Sandler. Canadian journal of mathematics, Tome 22 (1970) no. 3, p. 518. doi: 10.4153/CJM-1970-059-7
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[1] 1. Dembowski, P., Freie und offene projektive Ebenen, Math. Z. 72 (1960), 410–438. Google Scholar

[2] 2. Sandler, R., On finite collineation groups of F Can. J. Math. 21 (1969), 217–221. Google Scholar

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