# Create quotient group of units of mod n

I would like to work with the group $\mathbb{Z}_m^* / \langle p \rangle$. Do you know how I can create it?

For example:

```
p = 2
m = 17^2
Zm = ZZ.quotient(m) # ring of integers mod m
Zms = Zm.unit_group() # cyclic group (Z/mZ)^* generated by 3
Zms.quotient(p)
```

But the last line raises a `NotImplementedError`

.

There are a few issues. One is that quotients of arbitrary groups, even of arbitrary abelian groups, are not implemented. The second is that

`Zms`

doesn't remember that it is the group of units in`Zm`

— it is just an abstract multiplicative abelian group, cyclic of order 272 — so`p`

is not an element in it.Hi @JohnPalmieri. Yes, so even if I map p to an element of Zms, the command Zms.quotient will not work...

Quotients of additive cyclic groups are implemented, though:

`C272 = groups.misc.AdditiveCyclic(272)`

and then`C272.quotient(...)`

works.