Supersolvable Group
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvability is stronger than the notion of solvability.Let G be a group. G is supersolvable if there exists a normal series \{1\} = H_0 \triangleleft H_1 \triangleleft \cdots \triangleleft H_{s-1} \triangleleft H_s = G such that each quotient group H_{i+1}/H_i \; is cyclic and each Hi is normal in G.By contrast, for a solvable…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvability is stronger than the notion of solvability.Let G be a group. G is supersolvable if there exists a normal series \{1\} = H_0 \triangleleft H_1 \triangleleft \cdots \triangleleft H_{s-1} \triangleleft H_s = G such that each quotient group H_{i+1}/H_i \; is cyclic and each Hi is normal in G.By contrast, for a solvable group the definition requires each quotient to be abelian. In another direction, a polycyclic group must have a normal series with each quotient cyclic, but there is no requirement that each Hi be normal in G. As every finite soluble group is polycyclic, this can be seen as one of the key differences between the definitions.