Torsion subgroup of nilpotent group
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Suppose is a nilpotent group. The torsion subgroup of is defined in the following equivalent ways:
- It is the subset comprising all the elements of that have finite order. This subset turns out to be a subgroup.
- It is the largest subgroup of that is a periodic nilpotent group.
- It is the subgroup generated by all the elements in that have finite order.
Equivalence of definitions
This follows from equivalence of definitions of periodic nilpotent group.