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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 2

Question

Math 6310 • Algebra Summer 2020 • Question 2

Suppose \(G\) is a finitely generated Abelian group such that the automorphism group of \(G\) is finite. Let \(T\) be the torsion subgroup of \(G\). Describe all possibilities for \(G/T\) up to isomorphism.

Raw LaTeX

Suppose \(G\) is a finitely generated Abelian group such that the automorphism group of \(G\) is
finite. Let \(T\) be the torsion subgroup of \(G\). Describe all possibilities for \(G/T\) up to
isomorphism.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions Finite Group Theory Normal Subgroups and Commutator Subgroups