# 2-powered 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-powered group if it is powered over the prime 2, i.e., the square map is bijective from the group to itself, or equivalently, every element has a unique square root. Equivalently, the group is powered over the ring $\mathbb{Z}[1/2]$.

## Relation with other properties

### Conjunction with other properties

Conjunction Other component of conjunction Intermediate notions
Baer Lie group group of nilpotency class two 2-powered nilpotent group|FULL LIST, MORE INFO

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions