Geodesic
SEMILINEARTRANSFORMATIONS OVER FINITE FIELDS ARE FROBENIUS MAPS
Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 289-295

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

In its originalformulation Lang's theorem referred to a semilinear map on an n-dimensional vectorspace over the algebraic closure of GF(p): it fixes the vectors of a copy ofV(n, p^h). In other words, every semilinear map defined over a finite field isequivalent by change of coordinates to a map induced by a field automorphism. We provide an elementaryproof of the theorem independent of the theory of algebraic groups and, as a by-product of ourinvestigation, obtain a convenient normal form for semilinear maps. We apply our theorem to classicalgroups and to projective geometry. In the latter application we uncover three simple yet surprisingresults. 
DEMPWOLFF, U.; FISHER, J.CHRIS; HERMAN, ALLEN. SEMILINEARTRANSFORMATIONS OVER FINITE FIELDS ARE FROBENIUS MAPS. Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 289-295. doi: 10.1017/S0017089500020164
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     title = {SEMILINEARTRANSFORMATIONS {OVER} {FINITE} {FIELDS} {ARE} {FROBENIUS} {MAPS}},
     journal = {Glasgow mathematical journal},
     pages = {289--295},
     year = {2000},
     volume = {42},
     number = {2},
     doi = {10.1017/S0017089500020164},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500020164/}
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