Certain m.o.l.s. as groups

Longyear, Judith Q.

doi:10.1090/S0002-9939-1972-0307943-0

Certain m.o.l.s. as groups
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by Judith Q. Longyear PDF

Proc. Amer. Math. Soc. 36 (1972), 379-384 Request permission

Abstract:

It is shown that latin squares may be composed in a natural way, and that many sets of mutually orthogonal latin squares (m.o.l.s.) connected with projective planes may be regarded as groups of m.o.l.s. An axiom T6 is given for ternary rings. If T6 is true for a given ring, then the associated projective plane has prime power order; thus if T6 is a consequence of the definition for ternary rings, all projective planes have prime power order.

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