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On the fixed points of Sylow subgroups of transitive permutation groups

Published online by Cambridge University Press:  09 April 2009

Marcel Herzog  and
Cheryl E. Praeger
Marcel Herzog
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, Australia2600.
Cheryl E. Praeger
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, Australia2600.
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Abstract

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Let G be a transitive permutation group on a set Ω of n points, and let P be a Sylow p-subgroup of G for some prime p dividing ∣G∣. If P has t long orbits and f fixed points in Ω, then it is shown that f ≦ tp − ip(n), where ip(n) = p – rp(n), rp(n) denoting the residue of n modulo p. In addition, groups for which f attains the upper bound are classified.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 428 - 437
Copyright
Copyright © Australian Mathematical Society 1976

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