Representing matrices of almost completely decomposable groups

Almost completely decomposable groups can be described in terms of integral matrices and in terms of anti-representations in finite modules over prope r quotient rings of the ring of integers, The anti-representations are desc ribed by the so-called representating matrices. Representing matrices and t heir interrelationship with the integral matrices describing a group are st udied in general. It is shown that the integral and representing matrices m ay be assumed to have a special form. Two applications demonstrate the usef ulness of the results. (C) 2001 Elsevier Science B.V. All rights reserved.