2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119378We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of essential dimension of symmetric groups and alternating groups over field of any characteristic.24 pagesAlgebraic GeometryGroup Theory12E05, 12F10, 12F20, 13F30text