On irreducible n-ary quasigroups with reducible retracts

Details On irreducible n-ary quasigroups with reducible retracts On irreducible n-ary quasigroups with reducible retracts

2006-07-31

arxiv.org/abs/math/0607785v2

Eur. J. Comb. 29(2) 2008, 507-513

Mathematics

Combinatorics

8 p., 1 fig., ACCT-10. v2: revised, the figure improved

Scientific paper

10.1016/j.ejc.2007.01.005

An n-ary operation q:A^n->A is called an n-ary quasigroup of order |A| if in x_0=q(x_1,...,x_n) knowledge of any n elements of x_0,...,x_n uniquely specifies the remaining one. An n-ary quasigroup q is permutably reducible if q(x_1,...,x_n)=p(r(x_{s(1)},...,x_{s(k)}),x_{s(k+1)},...,x_{s(n)}) where p and r are (n-k+1)-ary and k-ary quasigroups, s is a permutation, and 1

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