Extremely primitive groups and linear spaces

Haiyan Guan; Shenglin Zhou

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 445-455
  • ISSN: 0011-4642

Abstract

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A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let 𝒮 be a nontrivial finite regular linear space and G ≤ Aut ( 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 ) ≥ 4 with few exceptions. Moreover, we show that Soc ( G ) is neither a sporadic group nor an alternating group, and G = PSL ( 2 , q ) with q + 1 a Fermat prime if Soc ( G ) is a finite classical simple group.

How to cite

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Guan, Haiyan, and Zhou, Shenglin. "Extremely primitive groups and linear spaces." Czechoslovak Mathematical Journal 66.2 (2016): 445-455. <http://eudml.org/doc/280092>.

@article{Guan2016,
abstract = {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 $G\le \{\rm Aut\}(\mathcal \{S\}).$ Suppose that $G$ is extremely primitive on points and let rank$(G)$ be the rank of $G$ on points. We prove that rank$(G)\ge 4$ 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.},
author = {Guan, Haiyan, Zhou, Shenglin},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear space; automorphism; point-primitive automorphism group; extremely primitive permutation group},
language = {eng},
number = {2},
pages = {445-455},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extremely primitive groups and linear spaces},
url = {http://eudml.org/doc/280092},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Guan, Haiyan
AU - Zhou, Shenglin
TI - Extremely primitive groups and linear spaces
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 445
EP - 455
AB - 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 $G\le {\rm Aut}(\mathcal {S}).$ Suppose that $G$ is extremely primitive on points and let rank$(G)$ be the rank of $G$ on points. We prove that rank$(G)\ge 4$ 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.
LA - eng
KW - linear space; automorphism; point-primitive automorphism group; extremely primitive permutation group
UR - http://eudml.org/doc/280092
ER -

References

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