On the maximum orders of elements of finite almost simple groups and primitive permutation groups
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- by Simon Guest, Joy Morris, Cheryl E. Praeger and Pablo Spiga PDF
- Trans. Amer. Math. Soc. 367 (2015), 7665-7694
Abstract:
We determine upper bounds for the maximum order of an element of a finite almost simple group with socle $T$ in terms of the minimum index $m(T)$ of a maximal subgroup of $T$: for $T$ not an alternating group we prove that, with finitely many exceptions, the maximum element order is at most $m(T)$. Moreover, apart from an explicit list of groups, the bound can be reduced to $m(T)/4$. These results are applied to determine all primitive permutation groups on a set of size $n$ that contain permutations of order greater than or equal to $n/4$.References
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Additional Information
- Simon Guest
- Affiliation: Centre for Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
- Address at time of publication: Peterborough Court, 133 Fleet Street, London EC4A 2BB, United Kingdom
- MR Author ID: 890209
- Email: guest.simon@gmail.com
- Joy Morris
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada
- Email: joy.morris@uleth.ca
- Cheryl E. Praeger
- Affiliation: Centre for Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia; Department of Mathematics, King Abdulazziz University, Jeddah, Saudi Arabia
- MR Author ID: 141715
- ORCID: 0000-0002-0881-7336
- Email: Cheryl.Praeger@uwa.edu.au
- Pablo Spiga
- Affiliation: Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy
- MR Author ID: 764459
- Email: pablo.spiga@unimib.it
- Received by editor(s): January 22, 2013
- Received by editor(s) in revised form: August 2, 2013
- Published electronically: March 23, 2015
- Additional Notes: The second author was supported in part by the National Science and Engineering Research Council of Canada
This research was supported in part by the Australian Research Council grants FF0776186 and DP130100106. - © Copyright 2015 by the authors
- Journal: Trans. Amer. Math. Soc. 367 (2015), 7665-7694
- MSC (2010): Primary 20B15, 20H30
- DOI: https://doi.org/10.1090/S0002-9947-2015-06293-X
- MathSciNet review: 3391897