torsion subgroup

English

Noun

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^[1]:

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