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

### J\'anos Ruff University of P\'ecs

#### Tam\'as Sz\H onyi E\"{o}tv\"{o}s Lor\'and University, Budapest

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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.

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