torsion subgroup

noun

(algebra) Subgroup of an abelian group whose generators have finite order.

The torsion subgroup of the group is finite.

意味（1）

(algebra) Subgroup of an abelian group whose generators have finite order.

A standard theorem about finitely generated abelian groups tells us that E(ℚ) looks like

qquad E(ℚ)≅( mbox FiniteGroup)⨯ underbrace {ℤ⨯ℤ⨯...⨯{Z_(r mbox copies)

qquad E(ℚ)≅E(ℚ)_(mbox tors)⨯ underbrace ℤ⨯ℤ⨯...⨯ℤ_(r mbox copies)

The finite subgroup E(ℚ)_(mbox tors) is called the

qquad color red mbox TorsionSubgroupofE(ℚ).}}