[GAP Forum] direct sums and counting subgroups

[Dmitrii Pasechnik]

surely you don't need GAP for solving this problem.
The answer is 3. There are 2 possibilities for an abelian group to be of
order p^2; one of them is realised only once, the other - twice.
I don't like giving more details, as this could be your homework :)


On 11/25/07 6:09 AM, "laurawicklund at comcast.net" <laurawicklund at comcast.net>
wrote:

> I recently installed GAP on my computer and am trying to figure out how to
> solve the following problem using GAP (I spent a few hours reading through the
> manual but haven't been successful).
> 
> Let p be prime.  Find the number of subgroups of order p^2 of the additive
> abelian group $G:=Z_{p^3}\oplus Z_{p^2}$
> 
> The group G is the direct sum of additive groups ZmodnZ(p^3) and ZmodnZ(p^2)
> 
> I would be content solving by problem for a specific p, say p=3.
> 
> Thank you for your time.
> 
> -Laura
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

-- 
Dima Pasechnik
http://www.ntu.edu.sg/home/dima/