Solvable line-transitive automorphism groups of finite linear spaces

2000 ◽  
Vol 43 (10) ◽  
pp. 1009-1013 ◽  
Author(s):  
Weijun Liu ◽  
Huiling Li
Keyword(s):  
Automorphism Groups ◽  
Linear Spaces ◽  
Transitive Automorphism ◽  
Finite Linear

Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

2017 ◽  
Vol 16 (06) ◽  
pp. 1750110
Author(s):  
Haiyan Guan ◽  
Shenglin Zhou
Keyword(s):  
Linear Space ◽  
Automorphism Groups ◽  
Linear Spaces ◽  
Finite Linear Space ◽  
Transitive Point ◽  
Finite Linear

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let [Formula: see text] be a non-trivial finite linear space with [Formula: see text] points, where [Formula: see text] and [Formula: see text] are two primes. We prove that if [Formula: see text] is line-transitive point-imprimitive, then [Formula: see text] is solvable.

Line-Transitive Automorphism Groups of Linear Spaces

1993 ◽  
Vol 25 (4) ◽  
pp. 309-315 ◽  
Author(s):  
Alan R. Camina ◽  
Cheryl E. Praeger
Keyword(s):  
Automorphism Groups ◽  
Linear Spaces ◽  
Transitive Automorphism

scholarly journals Line-transitive Automorphism Groups of Linear Spaces

10.37236/1227 ◽  
1995 ◽  
Vol 3 (1) ◽  
Author(s):  
Alan R Camina ◽  
Susanne Mischke
Keyword(s):  
Automorphism Group ◽  
Projective Plane ◽  
Linear Space ◽  
Automorphism Groups ◽  
Linear Spaces ◽  
Full Automorphism Group ◽  
Transitive Automorphism

In this paper we prove the following theorem. Let $\cal S$ be a linear space. Assume that $\cal S$ has an automorphism group $G$ which is line-transitive and point-imprimitive with $k < 9$. Then $\cal S$ is one of the following:- (a) A projective plane of order $4$ or $7$, (b) One of $2$ linear spaces with $v=91$ and $k=6$, (c) One of $467$ linear spaces with $v=729$ and $k=8$. In all cases the full automorphism group Aut(${\cal S} \!$) is known.

scholarly journals Geometrically rational real conic bundles and very transitive actions

2010 ◽  
Vol 147 (1) ◽  
pp. 161-187 ◽  
Author(s):  
Jérémy Blanc ◽  
Frédéric Mangolte
Keyword(s):  
Automorphism Groups ◽  
Algebraic Surfaces ◽  
Algebraic Models ◽  
Transitive Automorphism ◽  
Real Locus ◽  
Real Algebraic Surfaces ◽  
Conic Bundles ◽  
Transitive Actions ◽  
Insight Into

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

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