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Normal p-complements and fixed elements

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Abstract

We extend known results by proving that if an odd-order group acts on a 2-group and fixes all elements of order 2 and all real elements of order 4, then the action is trivial. We apply this to establish some 2-nilpotence criteria.

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Authors and Affiliations

  1. Mathematics Department, University of Wisconsin, 480 Lincoln Drive, Madison, WI, 53706, USA

    I. M. Isaacs

  2. Departament d’Algebra, Universitat de Valencia, 46100, Burjassot, Valencia, Spain

    Gabriel Navarro

Authors
  1. I. M. Isaacs
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  2. Gabriel Navarro
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Corresponding author

Correspondence to I. M. Isaacs.

Additional information

The second author was supported by the Spanish Ministry of Education, Grant MTM2007-61161.

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Isaacs, I.M., Navarro, G. Normal p-complements and fixed elements. Arch. Math. 95, 207–211 (2010). https://doi.org/10.1007/s00013-010-0162-9

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  • DOI: https://doi.org/10.1007/s00013-010-0162-9

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