The Iwasawa's Theorem - Mejía Alemán, Carlos (2021)
Let G be a group, Ω a set and K = {g ∈ G | ω * g = ω, Ɐω ∈ Ω} the nucleus of Ω where G acts on the set Ω. We will show that G/K is simple in the case that the group G verifies to be primitive on Ω, as well as that it is equal to its derived subgroup and finally if α ∈ Ω then Gα has a subgroup A that is abelian and normal such that G =< Ag | g ∈ G >, where Gα is the stabilizer of α in G. To finish we will give an application that the alternating group A5 is simple.