Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T21:34:59.678Z Has data issue: false hasContentIssue false
  • English
  • Français

On permutation groups with constant movement

Published online by Cambridge University Press:  09 April 2009

Mehdi Alaeiyan(Khayaty)
Mehdi Alaeiyan(Khayaty)
Affiliation:
Department of Mathematics Iran University of Science and TechnologyNarmak, Tehran 16844Iran e-mail: [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a permutation group on a set Ω with no fixed point in Ω. If for each subset Г of Ω the size |Гg - Г| is bounded, for g ∈ G, we define the movement of g as the max|Гg − Г| over all subsets Г of Ω. In particular, if all non-identity elements of G have the same movement, then we say that G has constant movement. In this paper we will first give some families of groups with constant movement. We then classify all transitive permutation groups with a given constant movement m on a set of maximum size.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 287 - 294
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Fein, B., Kantor, W. M. and Schacher, M., ‘Relative Brauer groups, II’, J. Reine Angew. Math. 328 (1981), 39–57.Google Scholar
[2]Gardiner, A. and Praeger, C. E., ‘Transitive permutation groups with bounded movement’, J. Algebra 168 (1994), 798–803.CrossRefGoogle Scholar
[3]Hassani, A., Khayaty, M., Khukhro, E. I. and Praeger, C. E., ‘Transitive permutation groups with bounded movement having maximal degree’, J. Algebra 214 (1999), 317–337.CrossRefGoogle Scholar
[4]Li, C. H., ‘The primitive permutation groups of certain degrees’, J. Pure Appl. Algebra 115 (1997), 275–287.Google Scholar
[5]Mann, A. and Praeger, C. E., ‘Transitive permutation groups of minimal movement’, J. Algebra 181 (1996), 903–911.Google Scholar
[6]Praeger, C. E., ‘On permutation groups with bounded movement’, J. Algebra 144 (1991), 436–442.CrossRefGoogle Scholar
[7]Praeger, C. E., ‘The separation problem for group actions’, in: Ordered groups and infinite permutation group (ed. Holland, W. C.) (Kluwer, Dordrecht, 1996) pp. 195–219.CrossRefGoogle Scholar
[8]Praeger, C. E., ‘Movement and separation of subsets of points under group action’, J. London Math. Soc. (2) 56 (1997), 519–528.CrossRefGoogle Scholar
[9]Rotman, J. J., An introduction to the theory of groups, 3rd edition (Allyn and Bacon, Boston, 1984).Google Scholar