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Characterizations of Finite Groups with \(\mathbf{P}\)-Fusion of Squarefree Type

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Abstract

For G a finite group and p a prime this paper proves two theorems under hypotheses that restrict the index of the subgroup generated by every p-element x in certain subgroups generated by pairs of its conjugates. Under one set of hypotheses G is shown to be supersolvable. Simple groups satisfying a complementary fusion-theoretic hypothesis are classified.

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Acknowledgements

The authors thank the referees for their careful reading of the paper, and their suggestions for improving its limpidity.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, VT, 05405, USA

    Richard Foote

  2. Department of Mathematical Sciences, University of Wisconsin Stevens Point, 2001 Fourth Ave., Stevens Point, WI, 54481, USA

    Matthew Welz

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  1. Richard Foote
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  2. Matthew Welz
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Correspondence to Richard Foote.

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Communicated by Ang Miin Huey.

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Foote, R., Welz, M. Characterizations of Finite Groups with \(\mathbf{P}\)-Fusion of Squarefree Type. Bull. Malays. Math. Sci. Soc. 40, 697–706 (2017). https://doi.org/10.1007/s40840-017-0448-1

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  • DOI: https://doi.org/10.1007/s40840-017-0448-1

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