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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Certain m.o.l.s. as groups


Author: Judith Q. Longyear
Journal: Proc. Amer. Math. Soc. 36 (1972), 379-384
MSC: Primary 05B15
MathSciNet review: 0307943
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0307943-0
PII: S 0002-9939(1972)0307943-0
Article copyright: © Copyright 1972 American Mathematical Society