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- W2004704048 abstract "A ternary quasigroup (or 3-quasigroup) is a pair (N, q) where N is an n-set and q(x, y, z) is a ternary operation on N with unique solvability. A 3-quasigroup is called 2-idempotent if it satisfies the generalized idempotent law: q(x, x, y) = q(x, y, x) = q(y, x, x)=y. A conjugation of a 3-quasigroup, considered as an OA(3, 4, n), , is a permutation of the coordinate positions applied to the 4-tuples of . The subgroup of conjugations under which is invariant is called the conjugate invariant subgroup of . In this article, we determined the existence of 2-idempotent 3-quasigroups of order n, n≡7 or 11 (mod 12) and n≥11, with conjugate invariant subgroup consisting of a single cycle of length three. This result completely determined the spectrum of 2-idempotent 3-quasigroups with conjugate invariant subgroups. As a corollary, we proved that an overlarge set of Mendelsohn triple system of order n exists if and only if n≡0, 1 (mod 3) and n≠6. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 292–304, 2010" @default.
- W2004704048 created "2016-06-24" @default.
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- W2004704048 date "2010-01-01" @default.
- W2004704048 modified "2023-09-26" @default.
- W2004704048 title "The spectrum of 2-idempotent 3-quasigroups with conjugate invariant subgroups" @default.
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- W2004704048 doi "https://doi.org/10.1002/jcd.20255" @default.
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