This talk is based on the class Makoto Matsumoto gave in the Arizona Winter School. To compute the Galois action on fundamental groups, it suffices to compute the element f_{sigma} for each sigma in G_Q. Consider the image of f_{sigma}, F_{sigma}=log(f_{sigma}^l), in the pro-l version of pi_1. Anderson, Coleman, and Ihara independently calculated the image in the quotient L'/[L',L'] involving the Soule's cocycle, using Jacobians of Fermat curve, Jacobi sums,etc. This talk will give a simple proof to verify some cases.