Let $p$ be a prime number. Is there a formula for the number of subgroups of
- $$\mathbb{Z}/p\mathbb{Z}\times \mathbb{Z}/p^2\mathbb{Z}$$
- $$\mathbb{Z}/p\mathbb{Z}\times \mathbb{Z}/p\mathbb{Z}\times\mathbb{Z}/p\mathbb{Z}$$
Thanks!
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$\begingroup$ Why the downvote? $\endgroup$– user95750Commented Dec 15, 2017 at 13:14
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2$\begingroup$ 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. $\endgroup$– Giuliano BiancoCommented Dec 15, 2017 at 13:30
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4$\begingroup$ Because MathOF is not a place for exercise (or exercise-level) questions. MathStackExchange is the right site for such questions. $\endgroup$– YCorCommented Dec 15, 2017 at 14:36
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$\begingroup$ @YCor, Thanks, yes it is easy ... I tried to remove the question but it doesn't work. $\endgroup$– user95750Commented Dec 15, 2017 at 20:28
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$\begingroup$ Maybe because there's an answer? this is (among others) why answering off-topic questions is discouraged. $\endgroup$– YCorCommented Dec 15, 2017 at 21:21
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1 Answer
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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. $\endgroup$ Commented Dec 15, 2017 at 13:30
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1$\begingroup$ 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