1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Different factorizations of p^n

  1. Feb 23, 2005 #1
    I was doing an exercise for my algebra class dealing with the number of abelian groups of order p^n, where p is a prime number, up to isomorphism. i had to fill out a table for n = 2 to n = 8. for example, for n = 2,3,4,5,6,7,8, the number of groups = 2,3,5,7,11,15,22, respectively. essentially, the different ways one can write p^n. for example, for p^5, one can write p^5, p^4 p, p^3 p p, etc... although not part of the question, i was wondering if there was an easy way to work out a formula for this relation given any n? seems interesting, but i haven't come across it yet.
  2. jcsd
  3. Feb 24, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Yes, these are partition numbers of some kind: the number of ways of writing n as the sum of integers.


    If you think about it an abelian p group is specified by the number of subgroups of order p, p squared, p cubed and so on, and it becomes clear where the numbers come from.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Different factorizations of p^n
  1. *p>n? set prime (Replies: 4)

  2. GL ( n , Z/p ) (Replies: 7)