Let P be a Sylow p- group of a finite group G and let H be a subgroup of G containing \( N_{G}(P) \) . Prove that \( H = N_{G}(H) \). Solution Let \( P \in Syl_{P}(G) \ and H \leq G \ such \ that \ N_{G}(P) \subset H \) Claim : Frattinis Argument : If G is a finite...

Rational function \( R(z)= \frac {P(z)}{Q(z)} \) ; where P and Q are polynimials . There are some theory about fixed points . Theorem: Let \( \rho \) be the fixed point of the maps R and g be the Mobius map . Then \( gRg^{-1} \) has the same number of fixed points at...

Understand the problem The sum of Infinity series ( 1 + frac{2}{3} + frac{6}{3^2} + frac{10}{3^3} + frac{14}{3^4} + …….) is Source of the problem Sample Questions(MMA) : 2018 Problem no 24 Topic Probability Difficulty Level Medium...