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December 4th, 2016, 02:39 AM  #1 
Member Joined: Oct 2013 Posts: 36 Thanks: 0  Last nontrivial group in the derived series of a solvable group
I was wondering if there were any special properties of the group $G^{(i1)}$ if $i$ is the smallest such integer such that $G^{(i)}$ is trivial for $G$ solvable. Clearly it must be abelian, but is it for example elementary abelian, can it contain a subgroup which is normal in $G$ etc. ?


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derived, group, nontrivial, series, solvable, trivial 
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