A influência dos subgrupos minimais na estrutura dos grupos finitos

Abstract

This dissertation is based on article "The influence of minimal subgroups of focal subgroups on the structure of finite groups" of X. Y. Guo and K. P. Shum, where they investigate the influence of the existence of complement of the minimal subgroups of a finite group G in the structure of the group. One result of Guo and Shum, says that if p is the smallest prime divisor of the order of a finite group G and P a Sylow p-subgroup of G and if every minimal subgroup of P ∩ G0 has a complement in NG(P), then G is p-nilpotent. In this work we will present the demonstration of this result, and give some applications of this theorem