Regular subgroups of the affine group and asymmetric product of radical braces

In this paper we introduce the asymmetric product of radical braces, a construction which extends the semidirect product of radical braces. This new construction allows to obtain rather systematic constructions of regular subgroups of the affine group and, in particular, our approach allows to put in a more general context the regular subgroups constructed by Hegedűs (2000) [9].