Generalized complete mappings, neofields, sequenceable groups and block designs. I

Derbiau Frank Hsu and A. Donald Keedwell

Vol. 111 (1984), No. 2, 317–332

DOI: 10.2140/pjm.1984.111.317

Abstract

The necessary and sufficient condition that the latin square formed by the Cayley multiplication table of a group has an orthogonal mate is that the group has a complete mapping. Here, we define two generalizations of the concept of a complete mapping and show how these generalizations are related to sequenceable groups and R-sequenceable groups respectively and that together they permit a complete characterization of left neofields. In the second part of the paper, we shall show that these generalizations also yield new constructions of block designs of Mendelsohn type.

Mathematical Subject Classification 2000

Primary: 20D60

Secondary: 05B30

Milestones

Received: 3 May 1982

Published: 1 April 1984