1. Limited time only! Sign up for a free 30min personal 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!

Abstract algebra- isomorphisms

  1. Feb 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Let [itex]A=C_{p^k}[/itex] where [itex]p[/itex] is a prime and [itex]k>0[/itex]. Let [itex]_{p^m} A [/itex]consist of all element a of A such that [itex]a^{p^m}=e[/itex].

    Prove that [itex]_{p^m} A/_{p^m-1} A\cong C_p[/itex] if [itex]m\leq k[/itex], [itex]\frac{_{p^m} A}{_{p^m-1} A}=e[/itex] if [itex]m>k[/itex]

    3. The attempt at a solution

    Please could someone explain how to get started with this proof, I have no idea.
  2. jcsd
  3. Feb 26, 2014 #2
    Have you heard of the first Isomorphism Theorem? That should do the trick.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Abstract algebra- isomorphisms