2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71265The Hopf order of an element $h$ of a Hopf algebra $H$ is the least $n$ such that the $n$-th Hopf power of $h$ is trivial. For some bismash product Hopf algebras obtained from factorizable groups (including Drinfeld doubles of some groups) we compute the dimensions of the spaces of elements with trivial $n$-th Hopf powers, and determine which Hopf orders of elements are possible. We discuss the behavior under twists and duality.28 pagesQuantum AlgebraRings and Algebras16W30text