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arXiv · 2003.00782

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

Wentang Kuo·Wei-Liang Sun
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Abstract

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 Jordan decomposition property when $m$ is congruent to $2$ modulo $4$. There are infinitely many such primes and these primes include the case $p \equiv 3 \pmod{4}$. We also prove that $\mathbb{Z}[Q_8 \times C_5]$ has the multiplicative Jordan decomposition property in a new way.

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Wentang Kuo, Wei-Liang Sun. 2020-03-02. The Multiplicative Jordan Decomposition in the Integral Group Ring $\mathbb{Z}[Q_8 \times C_p]$. https://doi.org/10.1016/j.jalgebra.2019.06.015

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