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On maximal abelian groups of maps

Published online by Cambridge University Press:  09 April 2009

Reinhard Winkler
Reinhard Winkler
Affiliation:
Institut für Algebra und Diskrete Mathematik, Technische Universität Wien, Wiedner Hauptstraß 8-10, 1040 Vienna, AUSTRIA
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Abstract

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The paper gives a rather simple description of all maximal abelian subgroups H of the symmetric group SM acting on an arbitrary set M. In the case of finite M this result is used to determine the maximal cardinality of such an H and the maximal number of permutations without fixed points contained in an abelian subgroup of SM.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 414 - 420
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bercov, R. and Moser, L., ‘On abelian permutation groups’, Canad. Math. Bull. 8 (1965), 627–630.CrossRefGoogle Scholar
[2]Tamaschke, O., Permutationsstrukturen (Bibliographisches Institut, Mannheim–Wien–Zürich, 1969).Google Scholar
[3]Wielandt, H., Finite Permutation Groups (Academic Press, New York, 1964).Google Scholar