torsion subgroup

Noun

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

Japanese Meaning

有限位数の生成元を持つアーベル群の部分群

有限生成アーベル群の研究では、有位数部分群は有限位数の元全体からなり、群の分解を決定します。

Sense（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).}}

torsion subgroups

（ plural ）