Open main menu

Groupprops β

2-torsion-free group

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