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

 

Inverse-cycles in weak-inverse loops


Author: R. Artzy
Journal: Proc. Amer. Math. Soc. 68 (1978), 132-134
MSC: Primary 20N05
MathSciNet review: 0463340
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Abstract: In a loop let J be the map taking every element into its right inverse. If the order of J is n, then $ \{ x,xJ, \ldots ,x{J^{n - 1}}\} $ is called an inverse-cycle of length n. If a weak-inverse loop consists only of the unit element and m inverse-cycles of length n, then n divides 2m.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0463340-4
PII: S 0002-9939(1978)0463340-4
Article copyright: © Copyright 1978 American Mathematical Society