[GAP Forum] Multiplicative Group modulo n

[Keshav Rao Kini]

Hello,

I'd just like to point out that the unit group of a field is the field less the additive identity, by definition - I'm not sure what field you are referring to here. "Units( ZmodnZ( n ) )" is probably what Johannes wants. It returns a group.

Yours,
    Keshav

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2010/12/5 Sandeep Murthy <sandeepr.murthy at gmail.com<mailto:sandeepr.murthy at gmail.com>>
Hi,

I think Units( R ), where R is a ring, will return the unit
group of a ring R, which is a multiplicative group.  A
field is a ring, so it should work.  According to the GAP
manual (p. 568), it will be returned either as a list or
group.  If the return is list, then you can always Group()
the list to make it a Group object.

Sincerely, Sandeep.

On 5 Dec 2010, at 13:57, Johannes Wachs wrote:

> Is there a way to call up the multiplicative group of order n?
>
> In particular I have written a program to output some set of positive
> integers. I want to test if they are a subgroup of the multiplicative group
> mod n. It would be great if I could use Subgroup(G, L);
>
> Alternatively, I think I could solve my problem by checking to see if my set
> is closed under multiplication mod n. Is there a way to implement IsGroup
> for some set mod n with multiplication?
>
> Johannes Wachs
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