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ISSN 1079-6762



Quasigroup associativity and biased expansion graphs

Author: Thomas Zaslavsky
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 13-18
MSC (2000): Primary 05C22, 20N05; Secondary 05B15, 05B35
Published electronically: February 10, 2006
MathSciNet review: 2200950
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Abstract: We present new criteria for a multary (or polyadic) quasigroup to be isotopic to an iterated group operation. The criteria are consequences of a structural analysis of biased expansion graphs. We mention applications to transversal designs and generalized Dowling geometries.

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Additional Information

Thomas Zaslavsky
Affiliation: Binghamton University, Binghamton, New York 13902-6000

Keywords: Multary quasigroup, polyadic quasigroup, factorization graph, generalized associativity, biased expansion graph, transversal design, Dowling geometry
Received by editor(s): September 15, 2004
Published electronically: February 10, 2006
Additional Notes: Research partially assisted by grant DMS-0070729 from the National Science Foundation.
Communicated by: Efim Zelmanov
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.