The Socle of Automorphism Groups of Linear Spaces

1996 ◽  
Vol 28 (3) ◽  
pp. 269-272 ◽  
Author(s):  
Alan R. Camina
Keyword(s):  
Automorphism Groups ◽  
Linear Spaces

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.

Sign in / Sign up

Export Citation Format

Share Document