Permutation-like matrix groups Original Research Article

Let image be a group of complex n × n matrices. We call image a permutation-like group if every matrix in image is similar to a permutation matrix. We consider the question whether a permutation-like group is equivalent to a group of permutation matrices. Examples show that this is not always the case. We investigate this problem in detail for some small values of n and conjecture that under some additional condition the above implication holds.