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Revision difference : solvable group
Version current Version 6
A group $G$ is {\em solvable} if it has a subnormal series A group $G$ is {\em solvable} if it has a subnormal series
$$ $$
G = G_0 \supset G_1 \supset \cdots \supset G_n = \{1\} G = G_0 \supset G_1 \supset \cdots \supset G_n = \{1\}
$$ $$
where all the quotient groups $G_i/G_{i+1}$ are abelian. where all the quotient groups $G_i/G_{i+1}$ are abelian.