2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105010We show that the problem of computing the distance of a given permutation from a subgroup $H$ of $S_n$ is in general NP-complete, even under the restriction that $H$ is elementary Abelian of exponent 2. The problem is shown to be polynomial-time equivalent to a problem related to finding a maximal partition of the edges of an Eulerian directed graph into cycles and this problem is in turn equivalent to the standard NP-complete problem of Boolean satisfiability.6 pages, 5 figuresCombinatorics20B40; 05C38, 20B35, 68Q25text