Finite Groups Represented by Special Matrices
G. A. Miller · Transactions of the American Mathematical Society · 1916
The direct object of this paper is to prove that every possible finite group which contains an abelian subgroup of half its own order can be represented by square matrices all of whose elements are equal to zero with the exception of those which appear in one of the diagonals, and these are all ordinary complex numbers.The fact that every finite group which can be represented by such matrices must contain an abelian subgroup of half its own order is at.once evident.The proof of the stated theorem may be based upon several interesting theorems relating to a possible choice of the independent generators of an abelian group.As these auxiliary theorems seem to be quite fundamental, we proceed to develop them in a somewhat more general form than would be necessary for the particular application in view.