The Multiplicative Jordan Decomposition in the Integral Group Ring $\mathbb{Z}[Q_8\times C_p]$

Wentang Kuo, Wei-Liang Sun

Let $p$ be a prime such that the multiplicative order $m$ of $2$ modulo $p$ is even. We prove that the integral group ring $\mathbb{Z}[Q_8\times C_p]$ has the multiplicative Jorda…