Quasi-orthogonal subalgebras of matrix algebras

In this paper, we investigate pairwise quasi-orthogonal subalgebras in Mpkn which are isomorphic to Mpk for k⩾1, n⩾2 and a prime number p with p⩾3. We prove there exist (p2kn-1)/(p2k-1) such subalgebras and they span Mpkn.