2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145633We investigate pairwise quasi-orthogonal subalgebras in $M_{p^{kn}}$ which are isomorphic to $M_{p^{k}}$ for $k \ge 1$, $n \ge 2$ and a prime number $p$ with $p \ge 3$. We prove there exist $p^{2kn}-1/p^{2k}-1$ such subalgebras and they span $M_{p^{kn}}$.12pagesOperator AlgebrasMathematical Physics15A30; 81R05text