The Iwasawa's Theorem
DOI:
https://doi.org/10.15381/pesquimat.v24i1.20511Keywords:
action, transitive, primitive group, block and kernelAbstract
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.
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Copyright (c) 2021 Carlos Mejía Alemán, Mario Enrique Santiago Saldaña
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