Unformatted text preview: k = ij . This group has a unique element of order 2 – ﬁnd it. What does Section 6 Exercise 50 say about this element? Remarks The group you are computing is called the group of quaternion units or sometimes just the quaternion group, and it makes a notable appearance in Math 120B. It is the smallest non-abelian group that satisﬁes the hypothesis of Section 6, Exercise 50 3. Using equation (1) on p.62 and the fact that there are inﬁnitely many prime numbers, show that the group Q of rational numbers under addition is not ﬁnitely generated....
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- Spring '09
- Integers, Prime number, residue classes