hw24 - G | mx = 0 } and if p is a prime we dened G ( p ) =...

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Modern Algebra 1 Homework 12.1 Spring 2010 Due April 21 Exercise 1. How many abelian groups are there of order n if n = 2008 , 2009 , 2010 or 2011? Exercise 2. Let G be an abelian group (written additively). Recall that for m N we defined G m = { x
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Unformatted text preview: G | mx = 0 } and if p is a prime we dened G ( p ) = { x G || x | is a power of p } . a. Prove that if n N and m | n then G m = ( G n ) m . b. Prove that G ( p ) = [ i =0 G p i ....
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