Math 2.0

Group theory and generalizations Finite groups Concept

Derived series

Summary

The derived series of a group is the sequence of iterated commutator subgroups G⊇G′⊇G′′⊇⋯G \supseteq G' \supseteq G'' \supseteq \cdots. A group is solvable if and only if this series reaches the trivial subgroup.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Commutator_subgroup, Derived series
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