Vol. 92, No. 2, 1981

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Partitions of groups and complete mappings

Richard J. Friedlander, Basil Gordon and Peter Tannenbaum

Vol. 92 (1981), No. 2, 283–293

Let G be an abelian group of order n and let k be a divisor of n1. We wish to determine whether there exists a complete mapping of G which fixes the identity element and permutes the remaining elements as a product of disjoint k-cycles. We conjecture that if G has trivial or noncyclic Sylow 2-subgroup then such a mapping exists for every divisor k of n1. Several special cases of the conjecture are proved in this paper. We also prove that a necessary condition for the existence of such a map holds for every k when G is cyclic.

Mathematical Subject Classification 2000
Primary: 20K99
Secondary: 20G99
Received: 12 September 1979
Revised: 8 April 1980
Published: 1 February 1981
Richard J. Friedlander
Basil Gordon
Peter Tannenbaum