torsion subgroup

torsion subgroup (plural torsion subgroups)

1. (algebra) Subgroup of an abelian group whose generators have finite order.
   • 2006 July 7, Joseph H. Silverman, An Introduction to the Theory of Elliptic Curves‎:

     A standard theorem about finitely generated abelian groups tells us that ${\displaystyle E(\mathbb {Q} )}$ looks like
     ${\displaystyle \qquad E(\mathbb {Q} )\cong ({\mbox{Finite Group}})\times \underbrace {\mathbb {Z} \times \mathbb {Z} \times ...\times \mathbb {Z} } _{r{\mbox{ copies}}}}$
     ${\displaystyle \qquad E(\mathbb {Q} )\cong E(\mathbb {Q} )_{\mbox{tors}}\times \underbrace {\mathbb {Z} \times \mathbb {Z} \times ...\times \mathbb {Z} } _{r{\mbox{ copies}}}}$
     The finite subgroup ${\displaystyle E(\mathbb {Q} )_{\mbox{tors}}}$ is called the
     ${\displaystyle \qquad \color {red}{\mbox{Torsion Subgroup of }}E(\mathbb {Q} ).}$