Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2001 • Question 7

Question

Math 6310 • Algebra Fall 2001 • Question 7

Let \(N\) be a positive integer. Prove that the natural map from \(\mathrm {SL}_2(\mathbb {Z})\) to \(\mathrm {SL}_2(\mathbb {Z}/N\mathbb {Z})\) is surjective.

Raw LaTeX

Let \(N\) be a positive integer. Prove that the natural map from \(\mathrm{SL}_2(\mathbb{Z})\) to
\(\mathrm{SL}_2(\mathbb{Z}/N\mathbb{Z})\) is surjective.

Topic Tags

Chinese Remainder Theorem and Product Decompositions