Abstract of article: Matrix groups over finite fields provide an excellent source of examples and computational problems in introductory presentations of abstract algebra. Students view arithmetic in these groups as natural. In addition, packages such as MATLAB may be used to verify group relations, find orders of elements, and count or display elements of subgroups.
Examples, problems, and experiments involving subgroups of GL(n, p), the group of invertible matrices over the integers mod p, are given that should strengthen intuition and understanding, heighten curiosity, and motivate subsequent theory. Nonabelian groups of the type rarely encountered in introductory presentations become available and accessible for student experimentation.
About the author: George Mackiw is Professor of Mathematical Sciences at Loyola College in Baltimore, Maryland. He did his undergraduate work at Georgetown University, Washington, D.C. and received his Ph.D. from the University of Virginia. In 1996 he was presented the Award for Distinguished College or University Teaching by the Maryland/D.C./Virginia Section of the Mathematical Association of America. His interests include abstract algebra, coding theory, linear algebra, and working with students.
Software used: MATLAB