Octonions, Albert vectors and the group $\mathrm{E}_6(F)

Communications in Algebra, 1-29, 2024 We present a uniform approach to the construction of the groups of type $\mathrm{E}_6$ over arbitrary fields without using Lie theory. This gives a simple description of the group generators and some of the subgroup structure. In the finite case our approach also permits relatively straightforward computation of the group order.