THE EXISTENCE OF OVERLARGE SETS OF
IDEMPOTENT QUASIGROUPS
常彦勋;雷建国
【期刊名称】《数学物理学报（英文版）》 【年(卷),期】2004(024)002
【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 Ax, x ∈ X based on X {x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups. 【总页数】6页(165-170) 【关键词】Pairwise
balanced
design;conjugate
invariant
subgroup;overlarge set of idempotent quasigroups 【作者】常彦勋;雷建国
【作者单位】Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China;Department of Mathematics, Hebei Normal University, Shijiazhuang 050091, China 【正文语种】中文 【中图分类】
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THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS
