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Fixed-point-free elements in p-groups

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Abstract

In this paper we prove that there exists no function F(m, p) (where the first argument is an integer and the second a prime) such that, if G is a finite permutation p-group with m orbits, each of size at least p F(m,p), then G contains a fixed-point-free element. In particular, this gives an answer to a conjecture of Peter Cameron; see [4], [6].

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, 35131, Via Trieste 63, Padova, Italy

    Eleonora Crestani & Pablo Spiga

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  1. Eleonora Crestani
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  2. Pablo Spiga
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Correspondence to Eleonora Crestani.

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Crestani, E., Spiga, P. Fixed-point-free elements in p-groups. Isr. J. Math. 180, 413–424 (2010). https://doi.org/10.1007/s11856-010-0109-7

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  • DOI: https://doi.org/10.1007/s11856-010-0109-7

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