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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2010 • Question 3

Question

Math 6310 • Algebra Fall 2010 • Question 3

Consider the automorphisms \(\sigma ,\tau \) of \(\mathbb {Q}(x)\) with \(\sigma :x\mapsto 1/x\) and \(\tau :x\mapsto 1-x\). What is the order of the group generated by these two elements? Determine the group.

Raw LaTeX

Consider the automorphisms \(\sigma,\tau\) of \(\mathbb{Q}(x)\) with
\(\sigma:x\mapsto 1/x\) and \(\tau:x\mapsto 1-x\). What is the order of the group generated by
these two elements? Determine the group.

Topic Tags

Galois Theory