#### Vol. 3, No. 1, 2006

 Recent Issues Volume 18 Volume 16 Volume 15 Volume 14 Volume 13 Volume 12 Volume 11 Volume 10 Volume 9 Volume 8 Volume 6+7 Volume 5 Volume 4 Volume 3 Volume 2 Volume 1
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN (electronic): 2640-7345 ISSN (print): 2640-7337 Author Index To Appear Other MSP Journals
Linear spaces with significant characteristic prime

### Nick Gill

Vol. 3 (2006), No. 1, 109–119
##### Abstract

Let $G$ be a group with socle a simple group of Lie type defined over the finite field with $q$ elements where $q$ is a power of the prime $p$. Suppose that $G$ acts transitively upon the lines of a linear space $\mathsc{S}$. We show that if $p$ is significant then $G$ acts flag-transitively on $\mathsc{S}$ and all examples are known.

##### Keywords
linear space, group of Lie type, line-transitive, parabolic subgroup
##### Mathematical Subject Classification 2000
Primary: 05B05, 20B25