(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A be a finite abelian group, prove # of subgps of order p = # of subgps of index p, p is a prime.

3. The attempt at a solution

I have thought about this probably very easy problem for 2 hours and could not find a

satisfying proof. I have tried bijective proof but failed

(sending <x> |-> A/<x> is fruitless), and I tried elementary

divisor decomposition

(writing A as G x Z_(p^(a_1))x... x Z_(p^(a_n)) x H, focusing

on the cyclic p-group part, and I have found that the number

of order p subgroups must be p^n - 1 in any such A) which I think is the right

direction but still can not work it out..T_T...please someone

please give me some hint please...please don't refer to too advanced a

theorem apart from the two abelian group decomposition theorems...thank you so much!!

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# Homework Help: Finite abelian group

Can you offer guidance or do you also need help?

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