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Improvement on the bounds of permutation groups with bounded movement

Published online by Cambridge University Press:  17 April 2009

Mehdi Alaeiyan
Mehdi Alaeiyan
Affiliation:
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran e-mail: [email protected]
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Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as, m := move(G) := supΓ{|Γg \ Γ| │ g ∈ G}. Let p be a prime, p ≥ 5. If G is not a 2-group and p is the least odd prime dividing |G|, then we show that n := |Ω| ≤ 4m – p + 3.

Moreover, if we suppose that the permutation group induced by G on each orbit is not a 2-group then we improve the last bound of n and for an infinite family of groups the bound is attained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 249 - 256
Copyright
Copyright © Australian Mathematical Society 2003

References

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