# Math Help - Quaternion Group

1. ## Quaternion Group

G={+/- 1, +/- i, +/- j, +/- k}
H={1, -1}

How do I construct the cayley table for G/H?

2. Originally Posted by jujab
G={+/- 1, +/- i, +/- j, +/- k}
H={1, -1}

How do I construct the cayley table for G/H?

The basic laws are: $i^2=j^2=k^2=-1\,,\,\,ij=k\,,\,\,jk=i\,,\,\,ki=j$ . Try now to have some fun proving that if you reverse the order of the above products you get minus the result, i.e. $ji=-k\,\,and\,\,etc.$

Tonio

3. Ok, thanks!