Magic Square Transformation Group

Let A = (a_i,j)_n×n (1≤i,j≤n) be a square matrix , including all elements of the set N = {1,2,3,..., n²} . If the sums of every row, every column and two diagonals are all n(n² + 1)/2 , then A is called the magic square of order N. In this thesis, we mainly investigate the transformations of the magic square and the transformation groups generated by which, furthermore the magic squares can be classified making use of the transformation groups.In Chapter 1 and Chapter 2, we shall give a brief introduction for the magic square and the concept of the transformation, also the group of the magic square of order three will be given. In Chapter 3, we represent the transformation groups of 8 and 32 orders, then the known 880 basic forms can be sorted into 220 differentforms; following the magic square of order four with special properties are developed, and the groups of 192 and 384 orders will be presented; In Chapter 4 , we shall give some corollaries about the classification of the magic squares of order four. In the last Chapter, we show the 220 and 9 different forms magic squares of order four.