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Let $p$ be a prime number. Is there a formula for the number of subgroups of

  1. $$\mathbb{Z}/p\mathbb{Z}\times \mathbb{Z}/p^2\mathbb{Z}$$
  2. $$\mathbb{Z}/p\mathbb{Z}\times \mathbb{Z}/p\mathbb{Z}\times\mathbb{Z}/p\mathbb{Z}$$

Thanks!

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  • $\begingroup$ Why the downvote? $\endgroup$
    – user95750
    Commented Dec 15, 2017 at 13:14
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    $\begingroup$ If I may guess, it was not me :-), because it is not so difficult to find the answer by a dutiful search on the web. Don't take it personally. $\endgroup$ Commented Dec 15, 2017 at 13:30
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    $\begingroup$ Because MathOF is not a place for exercise (or exercise-level) questions. MathStackExchange is the right site for such questions. $\endgroup$
    – YCor
    Commented Dec 15, 2017 at 14:36
  • $\begingroup$ @YCor, Thanks, yes it is easy ... I tried to remove the question but it doesn't work. $\endgroup$
    – user95750
    Commented Dec 15, 2017 at 20:28
  • $\begingroup$ Maybe because there's an answer? this is (among others) why answering off-topic questions is discouraged. $\endgroup$
    – YCor
    Commented Dec 15, 2017 at 21:21

1 Answer 1

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In the following bachelor thesis:

On p-groups of low power order

there is a chapter on subgroups, which includes the results you're searching for.

It is an useful work for beginners on p-groups.

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  • $\begingroup$ The link doesn't work with me : The requested URL /~boij/kandexjobbVT11/Material/pgroups.pdf. was not found on this server. $\endgroup$
    – user95750
    Commented Dec 15, 2017 at 13:30
  • $\begingroup$ try to google the title $\endgroup$ Commented Dec 15, 2017 at 13:31
  • $\begingroup$ I fixed the URL $\endgroup$ Commented Dec 15, 2017 at 13:41
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    $\begingroup$ Please don't answer exercise level questions that are not suitable for the site; it makes it impossible to remove them and hard to migrate. $\endgroup$ Commented Dec 15, 2017 at 23:01

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