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- Direct product of Sylow subgroups 1 answer
Questions like this have been asked before, but I just want some quick clarification on something.
Suppose that $G$ is the sum of its Sylow $p$-subgroups. Then each Sylow subgroup must be normal, and of course we have the other direction. If each Sylow subgroup is normal, then $G$ is the product of its Sylow subgroups.
My question that I need clarified is, "if $G$ is a sum of its Sylow subgroups, when will this be abelian, non-abelian?"