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<p>In this note, we provide some nilpotency criteria for the terms of the lower central series of a finite group involving the order of their standard generators. Moreover, when the finite group is solvable, we provide a characterization for the nilpotency of the terms of the derived series of the group.</p>

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Criteria for nilpotency of higher commutator subgroups

  • 期刊论文

  • 发表日期：

    2025年8月5日

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  • Raimundo Bastos,
  • William Cocke,
  • Carmine Monetta

摘要

In this note, we provide some nilpotency criteria for the terms of the lower central series of a finite group involving the order of their standard generators. Moreover, when the finite group is solvable, we provide a characterization for the nilpotency of the terms of the derived series of the group.