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

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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.

Facts

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
group of finite exponent |FULL LIST, MORE INFO
residually finite group |FULL LIST, MORE INFO
group embeddable in a finitary symmetric group |FULL LIST, MORE INFO
free group Residually finite group|FULL LIST, MORE INFO