Authors: Leroy B. Beasley and Larry Cummings
Journal: Proc. Amer. Math. Soc. 34 (1972), 351-355
MSC: Primary 15A15
MathSciNet review: 0419474
Abstract: A permanent group is a group of nonsingular matrices on which the permanent function is multiplicative. Let denote the Hadamard product of matrices A and B. The set of groups G of nonsingular matrices which contain the diagonal group and such that for every pair A, B of matrices in G we have is denoted by .
If the underlying field has at least three elements then consists of permanent groups. A partial converse is available:
If a permanent group G is generated by together with a set S of elementary matrices and a set Q of permutation matrices then where H is the subgroup generated by Q and K is generated by and S, and .
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