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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  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: [2 problems] Number of abelian groups and density of pri Quote:
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.  

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abelian, density, groups, number, primes, problems 
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