Let G be a group of order 99. Show that G must be abelian. (Hint: Prove that G is a direct product of Sylow subgroups.)
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First, we find the Sylow subgroups of G. Since the order of G is 99, we have that $|G|=3^2\cdot 11$. By the Sylow theorems, there exists a Sylow 3-subgroup P of order 9 and a Sylow 11-subgroup Q of order 11. Show more…
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