Abstract :
67584 Abstract. Let V be a vector space over a field F of characteristic p > 0 and let T be a regular subgroup of the affine group AGL(V ). In the finite dimensional case we show that, if T is abelian or p > 0, then T is unipotent. For T abelian, pushing forward some ideas used in [A. Caranti, F. Dalla Volta and M. Sala, Abelian regular subgroups of the affine group and radical rings, Publ. Math. Debrecen 69 (2006), 297{308.], we show that the set {t - I | t ? T} is a subalgebra of EndF(F V ), which is nilpotent when V has finite dimension. This allows a rather systematic construction of abelian regular subgroups.
