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Large sets of idempotent quasigroups with resolvability. (Chinese. English summary) Zbl 1488.05054

Summary: An idempotent quasigroup (IQ) possessing a unipotent orthogonal mate is called resolvable. An idempotent quasigroup possessing an idempotent orthogonal mate is called almost resolvable. A large set of idempotent quasigroups of order \(v\) is a partition of all 3-vectors with 3 distinct components of a \(v\)-set into \(v-2\) IQ(\(v\))s pairwise agreeing on only the idempotent rows. In this paper, large sets of resolvable idempotent quasigroups, large sets of almost resolvable idempotent quasigroups, and large sets of resolvable symmetric idempotent quasigroups (resolvable golf designs) are investigated by utilizing \(t\)-balanced designs with \(t=2,3\).

MSC:

05B30 Other designs, configurations
20N05 Loops, quasigroups
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