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- Different Applications of Sylow Theorems 3 answers
Almost all the books of algebra or group theory give following types of applications of Sylow theorems:
A group of order $...$ is not simple.
A group of order ... has normal Sylow subgroup.
Even in math.stackexchange, there are many questions with above title and they involve questions which are related to proving above type of statements.
Are there any other type of applications of these theorems of Sylow?