Vol. 40, No. 2, 1972

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An algebraic property of the totally symmetric loops associated with Kirkman-Steiner triple systems

A. Hedayat

Vol. 40 (1972), No. 2, 305–309
Abstract

The concept of an x-root of degree r in a loop of order n is introduced. It is shown that the totally symmetric loop of order n + 1 derived from any Kirkman-Steiner triple system of order n admits a maximal identity-root. A statisticalcombinatorial application of this algebraic property is then indicated. Finally, two open problems are also given.

Mathematical Subject Classification 2000
Primary: 05B15
Milestones
Received: 9 March 1970
Published: 1 February 1972
Authors
A. Hedayat