[GAP Forum] direct sums and counting subgroups

[Shaun Van Ault]

Dear Laura,
   The following seems to work, since these groups are abelian (Note, 
for group structures, CyclicGroup() is more appropriate than ZmodnZ()).

-Shaun Ault

> gap> G := DirectProduct(CyclicGroup(3^3), CyclicGroup(3^2));
> <pc group of size 243 with 5 generators>
> gap> n := Size(SubgroupsSolvableGroup(G));
> 36
> gap> 


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
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