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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: alaeiyan@iust.ac.ir, khayaty@iust.ac.ir
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Abstract

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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

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