Quasigroup Identities and Mendelsohn Designs
Quasigroup Identities and Mendelsohn Designs
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拟群恒等式和门德尔松设计
DOI：
10.4153/cjm-1989-017-0
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
F. Bennett
中科院分区：
文献类型：
--
作者：
F. Bennett
一个拟群是一个有序对（Q，·），其中Q是一个集合，（·）是Q上的一个二元运算，使得方程ax - B和ya - B对于Q中的每对元素a，B都是唯一可解的.众所周知（参见，例如，[11]），拟群的乘法表定义了拉丁方，也就是说，拉丁方可以被视为去掉标题和边线的拟群的乘法表。本文主要研究有限拟群。一个拟群（Q，·）称为幂等的，如果恒等式x2 = x对Q中的所有x成立.
A quasigroup is an ordered pair (Q, •), where Q is a set and (•) is a binary operation on Q such that the equations ax — b and ya — b are uniquely solvable for every pair of elements a,b in Q. It is well-known (see, for example, [11]) that the multiplication table of a quasigroup defines a Latin square, that is, a Latin square can be viewed as the multiplication table of a quasigroup with the headline and sideline removed. We are concerned mainly with finite quasigroups in this paper. A quasigroup (Q, •) is called idempotent if the identity x2 = x holds for all x in Q.