## Finite primitive groups and regular orbits of group elements

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- by Simon Guest and Pablo Spiga PDF
- Trans. Amer. Math. Soc.
**369**(2017), 997-1024 Request permission

## Abstract:

We prove that if $G$ is a finite primitive permutation group and if $g$ is an element of $G$, then either $g$ has a cycle of length equal to its order, or for some $r$, $m$ and $k$, the group $G \leq \mathrm {Sym}(m) \mathrm {wr}\mathrm {Sym}(r)$ preserves the product structure of $r$ direct copies of the natural action of $\mathrm {Sym}(m)$ on $k$-sets. This gives an answer to a question of Siemons and Zalesski and a solution to a conjecture of Giudici, Praeger and the second author.## References

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## Additional Information

**Simon Guest**- Affiliation: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- MR Author ID: 890209
- Email: simon.guest@imperial.ac.uk
**Pablo Spiga**- Affiliation: Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 55 Milano, MI 20125, Italy
- MR Author ID: 764459
- Email: pablo.spiga@unimib.it
- Received by editor(s): June 5, 2014
- Received by editor(s) in revised form: December 29, 2014, and February 2, 2015
- Published electronically: April 15, 2016
- Additional Notes: The second author is the corresponding author
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 997-1024 - MSC (2010): Primary 20B15, 20H30
- DOI: https://doi.org/10.1090/tran6678
- MathSciNet review: 3572262