论文标题
整体组环$ \ mathbb {z} [q_8 \ times c_p] $中的乘法约旦分解
The Multiplicative Jordan Decomposition in the Integral Group Ring $\mathbb{Z}[Q_8 \times C_p]$
论文作者
论文摘要
让$ p $成为一个素数，使得乘法订单$ m $ $ 2 $ modulo $ p $甚至是。我们证明，当$ m $一致至$ 2 $ modulo $ 4 $时，我们证明了整体组环$ \ mathbb {z} [q_8 \ times c_p] $具有乘法jordan empomposition属性。有许多这样的素数，这些素数包括$ p \ equiv 3 \ pmod {4} $。我们还证明，$ \ Mathbb {Z} [Q_8 \ Times C_5] $具有新的方式具有乘法Jordan分解属性。
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.
