Multiplicative Jordan Decomposition in Integral Group Ring of Group $K_8\times C_5$

Abstract

In this article, we present the multiplicative Jordan decomposition in integral group ring of group $K_8\times C_5$, where $K_8$ is the quaternion group of order 8. Thus, we give a positive answer to the question raised by Hales A W, Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II. J. Algebra, 2007, 316: 109–132".