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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2000 • Question 3

Question

Math 6310 • Algebra Fall 2000 • Question 3

Find an integer \(n\) such that the abelian group \(\mathbb {Z}/2\mathbb {Z}\oplus \mathbb {Z}/4\mathbb {Z}\oplus \mathbb {Z}/8\mathbb {Z}\) is a quotient of the multiplicative group \((\mathbb {Z}/n\mathbb {Z})^*\) of integers relatively prime to \(n\) modulo \(n\).

Raw LaTeX

Find an integer \(n\) such that the abelian group
\(\mathbb{Z}/2\mathbb{Z}\oplus\mathbb{Z}/4\mathbb{Z}\oplus\mathbb{Z}/8\mathbb{Z}\) is a quotient
of the multiplicative group \((\mathbb{Z}/n\mathbb{Z})^*\) of integers relatively prime to \(n\)
modulo \(n\).

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions Chinese Remainder Theorem and Product Decompositions Ideals and Quotient Rings