Quasigroup associativity and biased expansion graphs

Thomas Zaslavsky

doi:10.1090/S1079-6762-06-00155-7

Quasigroup associativity and biased expansion graphs

Thomas Zaslavsky

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	13-18
Number of pages	6
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	12
Issue number	2
DOIs	https://doi.org/10.1090/S1079-6762-06-00155-7
State	Published - Feb 10 2006

Keywords

Biased expansion graph
Dowling geometry
Factorization graph
Generalized associativity
Multary quasigroup
Polyadic quasigroup
Transversal design

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10.1090/S1079-6762-06-00155-7

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title = "Quasigroup associativity and biased expansion graphs",

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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KW - Biased expansion graph

KW - Dowling geometry

KW - Factorization graph

KW - Generalized associativity

KW - Multary quasigroup

KW - Polyadic quasigroup

KW - Transversal design

UR - https://www.scopus.com/pages/publications/33845466980

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JF - Electronic Research Announcements of the American Mathematical Society

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ER -

Quasigroup associativity and biased expansion graphs

Abstract

Keywords

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