Difference between revisions of "Torsion subgroups of elementary equivalent abelian groups are elementarily equivalent"

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(Created page with '==Statement== Suppose <math>G</math> and <math>H</math> are fact about::abelian groups that are elementarily equivalent. Then,…')
 
 
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==Statement==
 
==Statement==
  
Suppose <math>G</math> and <math>H</math> are [[fact about::abelian group]]s that are [[fact about::elementarily equivalent groups|elementarily equivalent]]. Then, their torsion subgroups, i.e., the subgroups comprising the elements that have finite [[order of an element|order]] (also called [[periodic element]]s or torsion elements) are also elementarily equivalent groups.
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Suppose <math>G</math> and <math>H</math> are [[fact about::abelian group]]s that are [[fact about::elementarily equivalent groups|elementarily equivalent]]. Then, their [[fact about::torsion subgroup]]s, i.e., the subgroups comprising the elements that have finite [[order of an element|order]] (also called [[periodic element]]s or torsion elements) are also elementarily equivalent groups.
  
 
==Related facts==
 
==Related facts==

Latest revision as of 21:54, 19 August 2009

Statement

Suppose G and H are Abelian group (?)s that are elementarily equivalent. Then, their Torsion subgroup (?)s, i.e., the subgroups comprising the elements that have finite order (also called periodic elements or torsion elements) are also elementarily equivalent groups.

Related facts