Answer to Question #23547 in Abstract Algebra for Hym@n B@ss

Question #23547

Let G be an f. c. group. Show that [G,G] is torsion

Expert's answer

If G is f. c., consider any g∈[G,G]. There exists a finitely generated subgroup H ⊆ G such that g ∈[H,H]. Since H is also f. c., the order of g divides|[H,H]| < ∞.

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