Abstract: Let F be any field,GL(m,F)be the general linear group over F,SF(m)be the set of orders of periodic elements in GL(m,F).Anecessary and sufficient condition for that there is an element A∈ GL(m,F)such that o(A)=n is proved.Moreover,if E/F is an extension of field,it is addressed a sufficient condition such that SF(m)=SE(m).