Abstract algebra- isomorphisms

  • Thread starter tom2014
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Homework Statement


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]


The Attempt at a Solution



Please could someone explain how to get started with this proof, I have no idea.
 

Answers and Replies

  • #2
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Have you heard of the first Isomorphism Theorem? That should do the trick.
 

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