TY - JOUR
T1 - A construction of one-dimensional affine flag-transitive linear spaces
AU - Pauley, M.J.
AU - Bamberg, John
PY - 2008
Y1 - 2008
N2 - The finite flag-transitive linear spaces which have an insoluble automorphism group were given a precise description in [Francis Buekenhout, Anne Delandtsheer, Jean Doyen, Peter B. Kleidman, Martin W. Liebeck, Jan Saxl, Linear spaces with flag-transitive automorphism groups, Geom. Dedicata 36 (1) (1990) 89–94], and their classification has recently been completed (see [Martin W. Liebeck, The classification of finite linear spaces with flag-transitive automorphism groups of affine type, J. Combin. Theory Ser. A 84 (2) (1998) 196–235] and [Jan Saxl, On finite linear spaces with almost simple flag-transitive automorphism groups, J. Combin. Theory Ser. A 100 (2) (2002) 322–348]). However, the remaining case where the automorphism group is a subgroup of one-dimensional affine transformations has not been classified and bears a variety of known examples. Here we give a construction of new one-dimensional affine flag-transitive linear spaces via the André/Bruck–Bose construction applied to transitive line-spreads of projective space.
AB - The finite flag-transitive linear spaces which have an insoluble automorphism group were given a precise description in [Francis Buekenhout, Anne Delandtsheer, Jean Doyen, Peter B. Kleidman, Martin W. Liebeck, Jan Saxl, Linear spaces with flag-transitive automorphism groups, Geom. Dedicata 36 (1) (1990) 89–94], and their classification has recently been completed (see [Martin W. Liebeck, The classification of finite linear spaces with flag-transitive automorphism groups of affine type, J. Combin. Theory Ser. A 84 (2) (1998) 196–235] and [Jan Saxl, On finite linear spaces with almost simple flag-transitive automorphism groups, J. Combin. Theory Ser. A 100 (2) (2002) 322–348]). However, the remaining case where the automorphism group is a subgroup of one-dimensional affine transformations has not been classified and bears a variety of known examples. Here we give a construction of new one-dimensional affine flag-transitive linear spaces via the André/Bruck–Bose construction applied to transitive line-spreads of projective space.
U2 - 10.1016/j.ffa.2007.07.006
DO - 10.1016/j.ffa.2007.07.006
M3 - Article
VL - 14
SP - 537
EP - 548
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
SN - 1071-5797
IS - 2
ER -