Re: Easy question in algebra
- From: quasi <quasi@xxxxxxxx>
- Date: Sat, 20 Aug 2005 20:55:17 -0700
On Sun, 21 Aug 2005 02:19:26 +0200, Anna Jansen
<ajansen77_spamfree@xxxxxx> wrote:
>Hi,
>
>I suppose this is an easy question in algebra:
>Let p,q be prime. Let further p=2q+1. Let g be an element of order q of
>the multiplicative group Z_p^*. So g is a generator of the order-q
>subgroup of Z_p^*. Every element h=g^x, for x \in {1, ..., q-1} is a
>generator of G. Is this correct? I suppose yes. Why is it not correct
>for x= q? Is the reason for that, that g^q =1 and 1 is not a generator of G?
>
>Thanks for your help
Yes and yes.
Your reasoning is correct.
In any group, 1 has order 1 no other element can have order 1.
In this subgroup, since q is prime and since the order of an element
must divide the order of any containing group, all elements other than
1 must have order exactly q, hence they generate the subgroup.
quasi
.
- References:
- Easy question in algebra
- From: Anna Jansen
- Easy question in algebra
- Prev by Date: St. Alphonsus Liguori on 7-7-04
- Next by Date: Re: question about axiomatic set theory
- Previous by thread: Easy question in algebra
- Next by thread: government employment-
- Index(es):
Relevant Pages
|
|
