TY - JOUR
T1 - Point-primitive generalised hexagons and octagons
AU - Bamberg, John
AU - Glasby, S. P.
AU - Popiel, Tomasz
AU - Praeger, Cheryl E.
AU - Schneider, Csaba
N1 - Funding Information:
The authors acknowledge the support of several Australian Research Council (ARC) grants: the Future Fellowship FT120100036 (JB), and the Discovery grants DP130100106 (JB, SG, CP) and DP140100416 (TP, CP, CS). The fifth author also acknowledges the hospitality of the Centre for the Mathematics of Symmetry and Computation (UWA) during his visit in July 2014, and funding from the research projects 302660/2013-5 (CNPq, Produtividade em Pesquisa), 475399/2013-7 (CNPq, Universal), and APQ-00452-13 (FAPEMIG, Universal).
Publisher Copyright:
© 2016
PY - 2017/4/1
Y1 - 2017/4/1
N2 - The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G2, D43, and F42. These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.
AB - The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G2, D43, and F42. These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.
KW - Generalised hexagon
KW - Generalised octagon
KW - Generalised polygon
KW - Primitive permutation group
UR - http://www.scopus.com/inward/record.url?scp=85003876189&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2016.11.008
DO - 10.1016/j.jcta.2016.11.008
M3 - Article
AN - SCOPUS:85003876189
SN - 0097-3165
VL - 147
SP - 186
EP - 204
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
ER -