Regular subgroups, nilpotent algebras and projectively congruent matrices

‎In this paper we highlight the connection between certain classes of regular subgroups of the affine group‎ ‎AGLn(F)‎, ‎F a field‎, ‎and associative nilpotent F-algebras of dimension n‎. ‎We also describe how the classification of projective congruence classes of square matrices is equivalent to the‎ ‎classification of regular subgroups of particular shap