Augmentation modules for affine groups - Brookes,CJB; Evans,DM (Mathematical Proceedings of the Cambridge Philosophical Society, 2001)
We prove that if k, F are fields of different characteristics then the permutation module kFn for the affine group AGL(n, F) has simple augmentation submodule. This proves a conjecture of A. R. Camina. © 2001 Cambridge Philosophical Society.