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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2001 • Question 11

Question

Math 6310 • Algebra Fall 2001 • Question 11

Let \(G\) be a finite abelian group and let \(n\) be an integer. Show that the map which sends \(g\) to \(ng\) is a group homomorphism and that it is an isomorphism if and only if \(n\) is relatively prime to the order of \(G\).

Raw LaTeX

Let \(G\) be a finite abelian group and let \(n\) be an integer. Show that the map which sends \(g\)
to \(ng\) is a group homomorphism and that it is an isomorphism if and only if \(n\) is relatively
prime to the order of \(G\).

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions Finite Group Theory Hom Functors and Module Homomorphisms