Abstract

The symbol GLH[m, n] will be used to represent the order of GLH(m, n), the group of linear transformations on m variables whose coefficients are taken modulo n in such a way that the determinant of each transformation is prime to n. In this note we state four theorems on congruence groups, which may be obtained by modifying proofs of corresponding theorems' on groups of transformations with coefficients in a Galois field GF[pn]. Theorem 5 gives a set of defining relations for a related abstract group.

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