Abstract
Groups of structure have an irreducible representation of degree 8 which can be realized over
and any prime field
This representation extends to a group of structure
Any subgroup
acts by scalar multiplication on this module over
In this short note we determine for which primes p > 7 and which Z the central products
and
have a regular orbit on the 8-dimensional
-module. This work was triggered by an omission in the paper [Citation4] by Köhler and Pahlings, a paper which is used in various places in work on the k(GV)-problem.
Keywords:
Acknowledgment
I thank Melissa Lee for making me aware of the gap concerning in the paper [Citation4]; this caused a corresponding gap in early versions of her article [Citation5] (which hopefully can now be closed).