Lattices generated by orbits of subspaces under the general linear group according to joints

Let F_q⁽ⁿ⁾ be the n-dimensional vector space over the finite field F_q , Let M (m,n) be any orbit of subspaces under GL_nF_q) , denote L(m,n) as the set of subspaces which are joins of subspaces in M(m,n) .This paper discusses the relation under the general linear group, with the condition that a subspace is an element of set generated by the given orbit, and when sets generated by orbits form geometric lattices.