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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2019 • Question 4

Question

Math 6310 • Algebra Spring 2019 • Question 4

Let \(n\ge 2\) be an integer. Prove that the natural map \(SL_2(\mathbb {Z})\longrightarrow SL_2(\mathbb {Z}/n)\) is surjective.

Raw LaTeX

Let \(n\ge 2\) be an integer. Prove that the natural map
\(SL_2(\mathbb{Z})\longrightarrow SL_2(\mathbb{Z}/n)\) is surjective.

Topic Tags

Chinese Remainder Theorem and Product Decompositions