Suppose that G is a finite group and G has a unique Sylow
Chapter 24, Problem 47E(choose chapter or problem)
Problem 47E
Suppose that G is a finite group and G has a unique Sylow p-subgroup for each prime p. Prove that G is the internal direct product of its nontrivial Sylow p-subgroups. If each Sylow p-subgroup is cyclic, is G cyclic? If each Sylow p-subgroup is Abelian, is G Abelian?
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