Extremely primitive groups and linear spaces
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 445-455.

Voir la notice de l'article dans Czech Digital Mathematics Library

A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let $\mathcal S$ be a nontrivial finite regular linear space and $G\leq {\rm Aut}(\mathcal S).$ Suppose that $G$ is extremely primitive on points and let rank$(G)$ be the rank of $G$ on points. We prove that rank$(G)\geq 4$ with few exceptions. Moreover, we show that ${\rm Soc}(G)$ is neither a sporadic group nor an alternating group, and $G={\rm PSL}(2,q)$ with $q+1$ a Fermat prime if ${\rm Soc}(G)$ is a finite classical simple group.
DOI : 10.1007/s10587-016-0267-9
Classification : 05B05, 05B25, 20B15, 20B25
Mots-clés : linear space; automorphism; point-primitive automorphism group; extremely primitive permutation group 
@article{10_1007_s10587_016_0267_9,
     author = {Guan, Haiyan and Zhou, Shenglin},
     title = {Extremely primitive groups and linear spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {445--455},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {2016},
     doi = {10.1007/s10587-016-0267-9},
     mrnumber = {3519613},
     zbl = {06604478},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0267-9/}
}
TY  - JOUR
AU  - Guan, Haiyan
AU  - Zhou, Shenglin
TI  - Extremely primitive groups and linear spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 445
EP  - 455
VL  - 66
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0267-9/
DO  - 10.1007/s10587-016-0267-9
LA  - en
ID  - 10_1007_s10587_016_0267_9
ER  - 
%0 Journal Article
%A Guan, Haiyan
%A Zhou, Shenglin
%T Extremely primitive groups and linear spaces
%J Czechoslovak Mathematical Journal
%D 2016
%P 445-455
%V 66
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0267-9/
%R 10.1007/s10587-016-0267-9
%G en
%F 10_1007_s10587_016_0267_9
Guan, Haiyan; Zhou, Shenglin. Extremely primitive groups and linear spaces. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 445-455. doi : 10.1007/s10587-016-0267-9. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0267-9/

Cité par Sources :