How Do Torsion Concepts Differ in Algebra and Differential Geometry?

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I wonder if there are some relationships between the torsion in algebra and the torsion in differential geometry. Could someone tell me something about them?
 

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Just to make sure we are talking about the same thing, torsion in algebra "measures" which elements of the group have finite order and torsion in geometry is a measure of how much a the curve "twists"?
 

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