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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.
     
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