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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 1

Question

Math 6310 • Algebra Fall 1998 • Question 1

Let \(q\) be a prime number. Show that the number of non-isomorphic abelian \(q\)-groups of order \(q^n\) is \(p(n)\), where \(p(n)\) denotes the number of partitions of \(n\).

Raw LaTeX

Let \(q\) be a prime number. Show that the number of non-isomorphic abelian \(q\)-groups of order
\(q^n\) is \(p(n)\), where \(p(n)\) denotes the number of partitions of \(n\).

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups