Signs on group Latin squares (Q1922541)

Each row and column of a Latin square, \(L\), of order \(n\) can be thought of as a permutation of the elements of an \(n\)-set. For \(L\), associate \(rc\in \{++,+-,-+,--\}\) where \(r\) (respectively \(c\)) is \(+\) if \(L\) has an even number of rows (respectively columns) that are odd permutations, and where \(r\) (respectively \(c\)) is \(-\) if \(L\) has an odd number of rows (respectively columns) that are odd permutations. In this paper, the authors study group Latin squares (obtained from the Cayley table of a finite group, \(G\)). The ordering of the elements does not affect the row or column signs. Among other results, the authors show that if \(|G|\equiv 2\pmod 4\) then \(rc=--\), otherwise \(rc=++\).