# 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*]*| < ∞*.Need a fast expert's response?

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