  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.
