# Quasigroup associativity and biased expansion graphs

```@article{Zaslavsky2006QuasigroupAA,
title={Quasigroup associativity and biased expansion graphs},
author={Thomas Zaslavsky},
journal={Electronic Research Announcements of The American Mathematical Society},
year={2006},
volume={12},
pages={13-18}
}```
• T. Zaslavsky
• Published 10 February 2006
• Mathematics
• Electronic Research Announcements of The American Mathematical Society
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. 1. Associativity in multary quasigroups A multary quasigroup is a set with an n-ary operation for some finite n ≥ 2, say f : Q → Q, such that the equation f(x1, x2, . . . , xn) = x0 is uniquely solvable for any one variable…
1 Citations
Associativity in multiary quasigroups: the way of biased expansions
A multiary (polyadic, n-ary) quasigroup is an n-ary operation which is invertible with respect to each of its variables. A biased expansion of a graph is a kind of branched covering graph with an

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