Abstract Algebra
《Abstract Algebra》 · 第 36 页 · Section 1.5「The Quaternion Group」
The quaternion group, $Q_8$, is defined by $Q_8=\{1,-1,i,-i,j,-j,k,-k\}$ with product $\cdot$ computed as follows: $1\cdot a=a\cdot1=a$, for all $a\in Q_8$; $(-1)\cdot(-1)=1$, $(-1)\cdot a=a\cdot(-1)=-a$, for all $a\in Q_8$; $i\cdot i=j\cdot j=k\cdot k=-1$; $i\cdot j=k$, $j\cdot i=-k$; $j\cdot k=i$, $k\cdot j=-i$; $k\cdot i=j$, $i\cdot k=-j$. […] Note that $Q_8$ is a non-abelian group of order $8$.