2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104972In this work we study the induction theory for Hopf group coalgebra. To reach this goal we define a substructure B of a Hopf group coalgebra $H$, called subHopf group coalgebra. Also, we introduced the definition of Hopf group suboalgebra and group coisotropic quantum subgroup of $H$.Quantum Algebra20G42,16W35, 81R50, 17B10text