2-torsion-free group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition
A group is termed a 2-torsion-free group if it is torsion-free for the prime number 2. Explicitly, this means that the group has no element of order two, or equivalently, it has no non-identity element whose order is a power of 2.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| 2-torsion-free nilpotent group | |FULL LIST, MORE INFO | |||
| 2-powered group | |FULL LIST, MORE INFO | |||
| 2-powering-injective group | |FULL LIST, MORE INFO | |||
| torsion-free group | |FULL LIST, MORE INFO |