Regular subgroups of the affine group and asymmetric product of radical braces. (Q267397)

\textit{M. W. Liebeck} et al. [Mem. Am. Math. Soc. 952 (2010; Zbl 1198.20002)] asked for a classification of all pairs \((G,B)\) where \(G\) is a finite permutation group and \(B\) a regular subgroup. An interesting class of examples for the affine case was given by \textit{P. Hegedűs} [J. Algebra 225, No. 2, 740-742 (2000; Zbl 0953.20040)]. The problem to classify regular subgroups of an affine group is equivalent to the classification of braces [\textit{F. Catino} and \textit{R. Rizzo}, Bull. Aust. Math. Soc. 79, No. 1, 103-107 (2009; Zbl 1184.20001)].NEWLINENEWLINE In the paper under review, the authors introduce the concept of asymmetric product of braces, a semidirect product twisted by a 2-cocycle. This sheds some light on Hegedűs' construction.