# Divisible not implies rationally powered

This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., divisible group) neednotsatisfy the second group property (i.e., rationally powered group)

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## Statement

It is possible for a divisible group (i.e., a group in which every element has a root for every ) to not be a rationally powered group (i.e., there is at least one element and one for which the root is not unique).

## Proof

The simplest example is the group of rational numbers modulo integers . We can also take the circle group . Also, any general linear group over the field of complex numbers (or in general, over any algebraically closed field of characteristic zero) satisfies the condition.