Let $G$ be a finite group of order $> 1$ . If $G$ is solvable, then how to show that $ G$ contains a nontrivial abelian subgroup normal in $G$ ?
$G$ be a finite solvable group of order more than $1$ , then $ G$ contains a nontrivial abelian subgroup normal in $G$?
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finite-groups
normal-subgroups
solvable-groups
1 Answers
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Let $n \geq 1$ be the smallest integer for which $D^n(G) = \{1\}$. Then $D^{n-1}(G)$ answers the question.
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0why is it abelian ? – 2017-02-19
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0$D(D^{n-1}(G)) = \{1\}$. – 2017-02-19