Finite Outer Automorphism Groups of Crystallographic Groups

Abstract

We present an algorithmic approach to the problem of calculating finite outer automorphism groups of crystallographic groups. As an intermediate product in the process, we get automorphism groups of those groups as well. In the special case of Bieberbach groups, the algorithm can be used to get information about the structure of symmetry groups of flat manifolds.

2000 AMS Subject Classification:

• Primary 20H15
• Secondary 20F34
• 57S30

Keywords:

• crystallographic group
• outer automorphism
• flat manifold
• symmetry

Acknowledgments

This research was supported by University of Gdańsk grant number BW - 5107-5-0345-0.