ON A SPECIAL LOOP, THE DICKSON FORM, AND THE LATTICE CONNECTED WITH $ O_7(3)$

Abstract

A special commutative Moufang loop of order is described. With the help of this loop, a trilinear Dickson form is constructed whose automorphism group is a Chevalley group of type . Next, with the help of , a 27-dimensional representation is constructed for over , . This makes it possible to prove anew the embedding . A similar construction concerning the embedding is described.