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Quasigroup associativity and biased expansion graphs
Author(s):
Thomas
Zaslavsky
Journal:
Electron. Res. Announc. Amer. Math. Soc.
12
(2006),
13-18.
MSC (2000):
Primary 05C22, 20N05;
Secondary 05B15, 05B35
Posted:
February 10, 2006
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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.
References:
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Additional Information:
Thomas
Zaslavsky
Affiliation:
Binghamton University, Binghamton, New York 13902-6000
Email:
zaslav@math.binghamton.edu
DOI:
10.1090/S1079-6762-06-00155-7
PII:
S 1079-6762(06)00155-7
Keywords:
Multary quasigroup,
polyadic quasigroup,
factorization graph,
generalized associativity,
biased expansion graph,
transversal design,
Dowling geometry
Received by editor(s):
September 15, 2004
Posted:
February 10, 2006
Additional Notes:
Research partially assisted by grant DMS-0070729 from the National Science Foundation.
Communicated by:
Efim Zelmanov
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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