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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Email:
zaslav@math.binghamton.edu

DOI:
https://doi.org/10.1090/S1079-6762-06-00155-7

Keywords:
Multary quasigroup,
polyadic quasigroup,
factorization graph,
generalized associativity,
biased expansion graph,
transversal design,
Dowling geometry

Received by editor(s):
September 15, 2004

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.