Vol. 52, No. 1, 1974

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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

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
Received: 12 December 1972
Published: 1 May 1974
Eugene Carlyle Johnsen
Thomas Frederick Storer