An idempotent Latin square of order $v$ is called resolvable and denoted by RILS(v) if the $v\left(v-1\right)$ off-diagonal cells can be resolved into $v-1$ disjoint transversals. A large set of resolvable idempotent Latin squares of order $v$, briefly LRILS(v), is a collection of $v-2$ RILS(v)s pairwise agreeing on only the main diagonal. In this article, an LRILS(v) is constructed for $v\in \left\{14,20,22,28,34,35,38,40,42,46,50,55,62\right\}$ by using multiplier automorphism groups. Hence, there exists an LRILS(v) for any positive integer $v\ge 3$, except $v=6$.

中文翻译：

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大组可解幂等拉丁方的谱

一个幂等的拉丁顺序平方$v$如果_ _$v\left(v-1\right)$非对角线单元格可以分解为$v-1$不相交的横断面。一大组可解幂等拉丁方阵$v$，简称 LRILS( v )，是一个集合$v-2$RILS( v ) 只在主对角线上成对地一致。在本文中，构造了一个 LRILS( v )$v\in \left\{14,20,22,28,34,35,38,40,42,46,50,55,62\right\}$通过使用乘数自同构群。因此，对于任何正整数都存在一个 LRILS( v )$v\ge 3$， 除了$v=6$.