2-torsion-free group

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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