(untitled) (Communications in Mathematical Research, 2020)
In this article, we present the multiplicative Jordan decomposition in integral group ring of group K_8× 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".