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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
Article

Abstract

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.

Keywords

Camina group Frobenius complement 

Mathematics Subject Classification

Primary 20D10 20D15 Secondary 20C15 

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References

  1. 1.
    Dark R., Scoppola C. M.: On Camina groups of prime power order. J. Algebra 181, 787–802 (1996)CrossRefMATHMathSciNetGoogle Scholar
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    Isaacs I. M.: Coprime group actions fixing all nonlinear irreducible characters. Canad. J. Math. 41, 68–82 (1989)CrossRefMATHMathSciNetGoogle Scholar
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    Lewis M. L.: Classifying Camina groups: a theorem of Dark and Scoppola. Rocky Mountain J. Math. 44, 591–597 (2014)CrossRefMATHMathSciNetGoogle Scholar
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    Macdonald I. D.: More on p-groups of Frobenius type. Israel J. Math. 56, 335–344 (1986)CrossRefMATHMathSciNetGoogle Scholar

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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