Sylow p-subgroups and its applications

Abstract

Let p be a prime st. pn devides order of a group G and pn+l does not divide it G. then a subgroup H of G s.t. O (H) = pn is called a sylow p-subgroup of G. there are three postulates of Sylow p-subgroups first theorem shows the existence of a sylow p-subgroup of G for every prime p dividing order of G while. Second theorem shows that any two sylow p-subgroups of G are conjugate and the third theorem says about the number of sylow p-subgroups of G.