Geodesic
Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 4, pp. 479-491.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we prove that there is no biplane admitting a flag-transitive automorphism group of almost simple type, with exceptional socle of Lie type. A biplane is a $( v, k,2)$-symmetric design, and a flag is an incident point-block pair. A group $G$ is almost simple with socle $X$ if $X$ is the product of all the minimal normal subgroups of $G$, and $X\? G\leq $Aut $( G)$. Throughout this work we use the classification of finite simple groups, as well as results from P.B. Kleidman's Ph.D. thesis which have not been published elsewhere.
Keywords: keywords automorphism group, flag-transitive, primitive group, symmetric design 
@article{JAC_2008__27_4_a1,
     author = {O'Reilly-Regueiro, Eugenia},
     title = {Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of {Lie} type.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {479--491},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__27_4_a1/}
}
TY  - JOUR
AU  - O'Reilly-Regueiro, Eugenia
TI  - Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.
JO  - Journal of Algebraic Combinatorics
PY  - 2008
SP  - 479
EP  - 491
VL  - 27
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2008__27_4_a1/
LA  - en
ID  - JAC_2008__27_4_a1
ER  - 
%0 Journal Article
%A O'Reilly-Regueiro, Eugenia
%T Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.
%J Journal of Algebraic Combinatorics
%D 2008
%P 479-491
%V 27
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2008__27_4_a1/
%G en
%F JAC_2008__27_4_a1
O'Reilly-Regueiro, Eugenia. Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 4, pp. 479-491. http://geodesic.mathdoc.fr/item/JAC_2008__27_4_a1/