# Subgroup of unit group

```
k = CyclotomicField(5)
U = k.unit_group()
v = U.gens()
u = U.gens_values()
T1 = U.subgroup([v[0]])
T2 = U.subgroup([u[0]])
```

This code attempts to generate a subgroup of the unit group of $\mathbb{Q}(\zeta_{5})$. The subgroup call for T1 works fine. The one for T2 breaks. This is close to bug #18863 that was already fixed, but this version of the problem persists.

The elements of u are recognized as elements of the group U. Still, Sage is unable to compute the subgroup generated by those elements. For my use case, it's important to manipulate the elements of u as elements in the field (including addition), which I don't think I can do with the elements of v.

Welcome to Ask Sage! Thank you for your question.