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Israel Journal of Mathematics

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

Dimension subgroups andp-th powers inp-groups

  • Lawrence E. Wilson
Article
  • 54 Downloads

Abstract

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.

Keywords

Positive Integer Normal Subgroup Repeated Application Nilpotence Class Lower Central Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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