| THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS |
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| 作者姓名： | 常彦勋 雷建国 |
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| 作者单位： | Chang Yanxun Department of Mathematics，Beijing Jiaotong University，Beijing 100044，China Lei Jianguo Department of Mathematics，Hebei Normal University，Shijiazhuang 050091，China |
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| 摘 要： | A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.
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| 关 键 词： | 存在性 幂等拟群 共轭不变子群 对称群 |
THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS |
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| Chang Yanxun.THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS[J].Acta Mathematica Scientia,2004,24(2):165-170. |
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| Authors: | Chang Yanxun |
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| Institution: | Chang Yanxun Department of Mathematics,Beijing Jiaotong University,Beijing 100044,China Lei Jianguo Department of Mathematics,Hebei Normal University,Shijiazhuang 050091,China |
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| Abstract: | A idempotent quasigroup (Q, o) of order n is equivalent to an n(n - 1) × 3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n 1)-set. Denote by T(n 1) the set of (n 1)n(n - 1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n 1) into n 1 n(n - 1) × 3 partial orthogonal arrays Ax, x ∈ X based on X \ {x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups. |
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| Keywords: | Pairwise balanced design conjugate invariant subgroup overlarge set of idempotent quasigroups |
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