# Group in which no non-identity element has arbitrarily large roots

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 in which no non-identity element has arbitrarily large roots is a group $G$ with the property that if $g$ is a non-identity element of $G$, there exists some natural number $n$ (dependent on $g$) such that the equation $x^n = g$ has no solution.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite group Group embeddable in a finitary symmetric group, Residually finite group|FULL LIST, MORE INFO