Regular subgroups, nilpotent algebras and projectively congruent matrices

Abstract

‎In this paper we highlight the connection between certain classes of regular subgroups of the affine group‎ ‎$AGL_n(F)$‎, ‎$F$ 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 shape‎.