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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2013 • Question 2

Question

Math 6310 • Algebra Spring 2013 • Question 2

Show that \((\mathbb {Q}/\mathbb {Z},+)\) has one and only one subgroup of order \(n\), for each integer \(n\ge 1\), and that this subgroup is cyclic.

Raw LaTeX

Show that \((\mathbb{Q}/\mathbb{Z},+)\) has one and only one subgroup of order \(n\), for each
integer \(n\ge 1\), and that this subgroup is cyclic.

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups