Re: problem in group theory
- From: mskirvin@xxxxxxxxx
- Date: 8 Dec 2005 17:03:22 -0800
tinaimp88@xxxxxxxxxxx wrote:
> I am trying to prove that the intersection of any two nontrivial
> subgroup of a infinite cyclic group is nontrivial. Let G=<g>
> If H=<g^n> , K=<g^m>, for n,m integers,(here n,m should be greater than
> 1)
> then HUK=<g^lcm(m,n)>, lcm(m,n)>1, so HUK is nontrivial.
> Am I on the right track to prove this problem?
> Thanks in advance!
Is HUK supposed to mean H intersect K? If you realize that H intersect
K is <g^lcm(m, n)>, then you're done. However, if HUK means H union K,
then you are mistaken. lcm(m, n) is strictly larger than at least one
of m and n, so H union K can't possibly be <g^lcm(m, n)> since there
would be elements of H or elements of K not in H union K.
Mike
.
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