# Quaternion Group

• November 3rd 2009, 03:14 PM
jujab
Quaternion Group
G={+/- 1, +/- i, +/- j, +/- k}
H={1, -1}

How do I construct the cayley table for G/H?
• November 4th 2009, 04:37 AM
tonio
Quote:

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
• November 4th 2009, 10:26 AM
jujab
Ok, thanks!