Group with at most n nth roots for any element

Definition
A group with at most n nth roots for any element is a group $$G$$ satisfying the following condition: for any $$g \in G$$, the number of solutions to $$x^n = g$$ is at most $$n$$.

Stronger properties

 * Weaker than::Multiplicative group of a field

Weaker properties

 * Stronger than::Group with at most n elements of order dividing n