J Austral Math Soc Ser A 55 pp414--420, 1993.

On Maximal Abelian Groups of Maps

Reinhard Winkler

Abstract

The paper gives a rather simple description of all maximal abelian subgroups H of the symmetric group S_M 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 S_M.

1991 AMS Subject Classification: 22B35

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Authors

Reinhard Winkler

Institut fur Algebra and Diskrete Mathematik, Technische Universitat Wien, Wiedner Hauptstrabe 8-10, 1040 Vienna, AUSTRIA.