Abstract Algebra: Theory and Applications · Problem 13.12

Group Actions — Thomas Judson

Mathematics — Abstract Algebra · finite-abelian-groups

Problem

A group

G

is a torsion group if every element of

G

has finite order. Prove that a finitely generated abelian torsion group must be finite. Hint. Use the Fundamental Theorem of Finitely Generated Abelian Groups.

Related theory

Fundamental Theorem Of Finite Abelian Groups

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