Michael K. Mahoney

Determinants of integral group matrices for some nonabelian 2-generator groups

The problem considered is to characterize those integers d such that d = det(A)Aan integral group matrix for a dihedral or metacyclic group G. For G=D m, the dihedral group of degree m, the integers d are characterized when m is an odd prime and the primes d are characterized when m≡ 2 mod 4. For a ZS-metacyclic group G of order n, it is shown that if a prime p divides (d,n) such that n and d= det(A) has solutions, then P t+1∥d. For both types of groups G we show that the order of G can never occur as the determinant of an integral group matrix for G.

Implementing a GKS-like graphics package on a microcomputer

A variable-length project for an introductory upper-division computer graphics course for majors is described. The project consists of the implementation of a graphics package based on the Graphical Kernel System (GKS, an ISO and ANSI standard) and application programs which demonstrate features of GKS. Any microcomputer with graphics capabilities equipped with an appropriate compiler can be used for the project. It is assumed that the reader is familiar with the basic concepts of 2D computer graphics. A brief introduction to GKS is included.