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    Cyclic groups are solvable

    E-AMD-KGEXBKIW

    Area
    Algebra
    Topics
    Cyclic Groups, Solvable Groups
    Status
    draft

    Show that every cyclic group is solvable.

    Solution

    Every cyclic group is abelian. Hence its commutator subgroup is trivial: \[ [G,G]=1. \] Therefore the derived series reaches the identity after one step, so \(G\) is solvable.

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