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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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.
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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:
  • Pablo Spiga
  • Affiliation: Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 55 Milano, MI 20125, Italy
  • MR Author ID: 764459
  • Email:
  • 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:
  • MathSciNet review: 3572262