Combinatorial structures in loops. II. Commutative inverse property cyclic neofields of prime-power order

Eugene Carlyle Johnsen and Thomas Frederick Storer

Vol. 52 (1974), No. 1, 115–127

DOI: 10.2140/pjm.1974.52.115

Abstract

In this paper we construct a large family of commutative inverse property, cyclic (CIP) neofields of prime-power order. Our purpose in doing so is to produce a class of algebraic systems which shall be useful in certain combinatorial constructions. One of these constructions is that of power-residue difference sets in the additive loops of finite CIP neofields which is a natural generalization of the corresponding constructions in the additive groups of finite fields. Another is that of cyclic Steiner triple systems, i.e., Steiner triple systems with a cyclic group of automorphisms sharply transitive on elements, which we discuss in the last section of this paper.

Mathematical Subject Classification 2000

Primary: 05B10

Secondary: 12K05

Milestones

Received: 12 December 1972

Published: 1 May 1974