Permanent Groups. II
LeRoy B. Beasley, Larry Cummings · Proceedings of the American Mathematical Society · 1973
A permanent group is a group of nonsingular matrices on which the permanent function is multiplicative. We consider only permanent groups which contain the group of nonsingular diagonal matrices. If the underlying field is infinite of characteristic zero or greater than $n$, then each such permanent group consists only of matrices in which exactly one diagonal has all nonzero entries.