Realizations of involutive automorphisms σ and Gσ of exceptional linear Lie groups G, part I, G=G₂. F₄ and E₆

classified involutive automorphisms σ of simple Lie algebras g and determined the type of the subalgebras gσ of fixed points. Now for connected exceptional universal linear Lie groups G , we shall find involutive automorphisms σ and realize the subgroups Gσ of fixed points explicitly. In this paper we consider the cases of type G₂, F₄ and E₆ . Our results are as follows. (Results of E₇ will be soon appeared in this Journal).