 My Math Forum [2 problems] Number of abelian groups and density of primes
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 January 10th, 2008, 12:17 PM #1 Newbie   Joined: Jan 2008 Posts: 2 Thanks: 0 [2 problems] Number of abelian groups and density of primes Hi there. I have two minor problems I would like to verify. If someone could please send me clues about the below problems I would be grateful. 1. How many different (up to isomorphism) abelian groups of cardinality 245 exist? It is just how to start problem, and why is it 245? 2. Calculate the density of primes in the arithmetic progression 10n + 3. Completely no idea how to start. I probably lack some important theorems. Thank You for clues. January 14th, 2008, 01:14 PM   #2
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Re: [2 problems] Number of abelian groups and density of pri

Quote:
 Originally Posted by Creebo Hi there. I have two minor problems I would like to verify. If someone could please send me clues about the below problems I would be grateful. 1. How many different (up to isomorphism) abelian groups of cardinality 245 exist? It is just how to start problem, and why is it 245? 2. Calculate the density of primes in the arithmetic progression 10n + 3. Completely no idea how to start. I probably lack some important theorems. Thank You for clues.
1. Cheaty answer: see this list for A000688.

The important thing to note is that this is a multiplicative function, so the number of a(245) of abelian groups of order 245 = a(5) * a(7^2), and a(p^n) = n for p prime.

2. the theorem you need is Dirichlet's theorem. Tags abelian, density, groups, number, primes, problems Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post JWhiz Advanced Statistics 0 November 4th, 2013 10:06 PM Math Amateur Abstract Algebra 0 October 29th, 2013 03:46 PM WORLD Number Theory 5 September 3rd, 2012 02:36 PM gaussrelatz Abstract Algebra 9 July 9th, 2012 09:09 AM Mai Abstract Algebra 2 June 6th, 2010 07:43 AM

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