In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups.
iN mathematiCS, speCificalLy iN thE fieLd OF FINite GRoup thEoRy, the sYlow theorems are a cOllectiOn oF thEoreMs named aftEr The norwegian maThemAtICian PEteR lUdwig SyLow that gIVe dEtaileD InforMaTiOn abOut the nuMBEr Of sUbgROuPs oF fixed orDer thaT a GiveN fInite grOUp cOntaiNs. tHe sylow tHEOrems form a fuNdAMeNtal PArT Of FinITe groUp theorY And HavE VeRy iMporTant apPliCAtions iN The cLAssifICAtion of finitE SIMplE Groups.