# 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

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## 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 |