Geodesic
Maximal Groups on Which the Permanent is Multiplicative
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 495-497

Voir la notice de l'article provenant de la source Cambridge University Press

Let Δn be the set of all n × n, non-singular matrices of the form PD, where P is a permutation matrix and D is a diagonal matrix with complex entries. In (1, conjecture 12), Marcus and Mine asked: Is Δn a maximal group on which the permanent function is multiplicative? (that is, per AB = per A per B). The field over which the entries range was not mentioned in the conjecture; however, we assume that the complex number field was intended. Corollary 1 answers this in the affirmative. In fact, Δn is the only maximal group (or semigroup) on which the permanent is multiplicative. Let ρi be the set of all non-zero entries in the ith row and let λj be the set of all non-zero entries in the jth column. 
Beasley, Leroy B. Maximal Groups on Which the Permanent is Multiplicative. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 495-497. doi: 10.4153/CJM-1969-055-2
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[1] 1. Marcus, M. and Mine, H., Permanents, Amer. Math. Monthly 72 (1965), 577–591. Google Scholar

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