Israel Journal of Mathematics

, Volume 138, Issue 1, pp 1–17 | Cite as

Dimension subgroups andp-th powers inp-groups

  • Lawrence E. Wilson


We prove that if the nilpotence class of ap-group is strictly less thanp kthen every product ofp k-thpowers can be written as thep-th power of an element. Scoppola and Shalev have proven the same thing for groups of class strictly less thanp kp k−1. They also provide an example which proves that ours is the best possible result. This is a generalization of the well known fact that in groups of class strictly less thanp every product ofp-powers is again ap-th power. Along the way we prove results of independent interest on dimension subgroups ofp-groups.


Positive Integer Normal Subgroup Repeated Application Nilpotence Class Lower Central Series 
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Copyright information

© The Hebrew University Magnes Press 2003

Authors and Affiliations

  • Lawrence E. Wilson
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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