In a latin square of order $n$, a near transversal is a collection of $n-1$ cells which intersects each row, column, and symbol class at most once. A longstanding conjecture of Brualdi, Ryser, and Stein asserts that every latin square possesses a near transversal. We show that this conjecture is true for every latin square that is main class equivalent to the Cayley table of a finite group.

中文翻译：

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所有基于组的拉丁方格都具有近横向

在 $n$ 阶的拉丁方格中，近横向是 $n-1$ 单元格的集合，这些单元格最多与每行、每列和符号类相交一次。Brualdi、Ryser 和 Stein 的一个长期猜想断言，每个拉丁方阵都有一个近乎横断面。我们证明了这个猜想对于每个主类等价于有限群的凯莱表的拉丁方都是成立的。