How do I find an isomorphism between Sn+m and Zn x Zm?

[clkt]

How do I find an isomorphism between Sn+m and Zn x Zm? provided n,m are not relatively prime? Thanks.

 

[AKG]

I dunno, place an ad in the classifieds, put up posters, etc. Or maybe start by defining what you even mean by Sn+m, because in the standard notation, Sn+m is a group that's generally not isomorphic to Zn x Zm. Also, post this in the homework section, follow the guidelines for posting homework, and when you start a new thread in the homework section, use the template that will be given to you.

 

[clkt]

Hi, this isn't exactly a homework question... Anyways, rereading my question again, I made a mistake. It should be how do I find an isomorphism between A SUBGROUP in Sn+m and Zn x Zm. If it is specific cases like n,m = 2,2 I can figure it out. But how do I figure out a general form for the isomorphism?

 

[StatusX]

If there are two subgroups H and K of a group G such that the intersection of H and K is trivial and hk=kh for all h in H, k in K, then the subgroup HK is isomorphic to HxK.

 

[clkt]

ah, thanks, I think I have it figured out now!