Characterization of the unit group of ℤ[G × C2n

Abstract

Let [Formula: see text] be a group and [Formula: see text] be the cyclic group of order 2. We characterize the unit group [Formula: see text] of the integral group ring [Formula: see text] in terms of the unit group [Formula: see text], for every positive integer [Formula: see text]. As a consequence, for each [Formula: see text], we determine conditions on some class of matrices [Formula: see text]s, to be in GL[Formula: see text]. Using this we calculate the integer solutions of some specific class of symmetric polynomial [Formula: see text] with integer coefficients.