Sobre el teorema PaQb de Burnside

Abstract

Utilizando herramientas de la teoría de representación de grupos finitos se muestra una interesante proposición sobre grupos de automorfismos de p-grupos abelianos elementales; con ayuda de este resultado presentamos una demostración del siguiente resultado de Burnside: Sea p y q dos números primos distintos y G un grupo finito de orden paqb. Si Pa Qb, entonces con un limitado y explícito número de excepciones, G debe tener un p-subgrupo normal no trivial. / Abstract. Using the tools of representation theory of finite groups shows an interesting proposition on groups of automorphisms of elementary abelian p-groups, with the help of this result we present a proof of the following result of Burnside: Let p and q two distinct prime numbers and G a finite group of order paqb. If Pa Qb, then with an explicit limited number of exceptions, G should have a normal p-subgroup is not trivial (Texto tomado de la fuente).

Using the tools of representation theory of finite groups shows an interesting proposition on groups of automorphisms of elementary abelian p-groups, with the help of this result we present a proof of the following result of Burnside: Let p and q two distinct prime numbers and G a finite group of order p a q b . If p a > qb , then with an explicit limited number of exceptions, G should have a normal p-subgroup is not trivial.