# Integral automorphisms of higher dimensional affine spaces over finite fields $GF(p)$

###
J\'anos Ruff

University of P\'ecs

####
Istv\'an Kov\'acs

University of Primorska, Koper

####
Klavdija Kutnar

University of Primorska, Koper

####
Tam\'as Sz\H onyi

E\"{o}tv\"{o}s Lor\'and University, Budapest

PDF

**Minisymposium:**
FINITE GEOMETRY

**Content:**
A permutation of the affine space $AG(n,q)$ is called an integral automorphism if it preserves the integral distance defined among the points.
The integral automorphisms which are also semiaffine transformations were determined by Kurz and Meyer (2009). In this talk, we show that there is no additional integral automorphism for the affine spaces
$AG(n,p)$ and $AG(3,p^2),$ where $n \ge 3$ and $p$ is an odd prime. Joint work with Istv\'an Kov\'acs, Klavdija Kutnar and Tam\'as Sz\H onyi.