Archiv der Mathematik

, Volume 104, Issue 5, pp 401–405 | Cite as

CAMINA p-groups that are generalized Frobenius complements

  • I. M. Isaacs
  • Mark L. Lewis


Let P be a Camina p-group that acts on a group Q in such a way that \({\mathbf{C}_P(x) \subseteq P'}\) for all nonidentity elements \({x \in Q}\). We show that P must be isomorphic to the quaternion group Q 8. If P has class 2, this is a known result, and this paper corrects a previously published erroneous proof of the general case.


Camina group Frobenius complement 

Mathematics Subject Classification

Primary 20D10 20D15 Secondary 20C15 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of WisconsinMadisonUSA
  2. 2.Department of Mathematical SciencesKent State UniversityKentUSA

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