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If a group $G$ is solvable, is the subnormal series (the chain of the normal subgroups) unique? Or what type of solvable groups have unique subnormal series?

nekodesu
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    Not sure on the second part, but any chain of subgroups of an abelian group will trivially be a subnormal series, and this is clearly not unique in general. In that light, a cheap example of solvable groups with unique subnormal series are prime order groups (why?). – J.G Apr 27 '16 at 23:49

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