带可分解性质的幂等拟群大集

Large sets of idempotent quasigroups with resolvability

具有幂单正交侣的幂等拟群称为可分解的.具有幂等正交侣的幂等拟群称为几乎可分解的.若v元集合上的所有分量互不相同的3-向量能够分拆成互不相交(幂等3-向量除外)的v2个v阶幂等拟群,则称之为v阶幂等拟群大集.本文使用t-平衡设计(t=2,3)的方法给出了可分解幂等拟群大集、几乎可分解幂等拟群大集及可分解对称幂等拟群大集(即可分解高尔夫设计)的构造方法,给出了其存在性的若干结果.

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.