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Abelian groups | Topic profile

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Latest threads on abelian groups:

HELP!!! Find all abelian groups (up to isomorphism)!!!

Started 2 weeks, 3 days ago (2009-11-24 02:08:00) by nalkapo

I am really confused on this topic. can you give me an example and explain how you found, pleaseee! for example, when i find abelian group of order 20; |G|=20 i will find all factors and write all of them, Z_20 (Z_10) * (Z_2) (Z_5)* (Z_2) * (Z_2) for higher order such as |G|=200 , i can't do this.(i did and it was wrong) can you tell me ...

Source: Physics Help and Math Help - Physics Forums

Forum: Linear & Abstract Algebra

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Re: HELP!!! Find all abelian groups (up to isomorphism)!!!

Started 3 days, 5 hours ago (2009-12-08 13:38:00) by Jamma

All finite abelian groups are of the form (Z_a)x(Z_b)x...x(Z_n) and anything of this form is a finite abelian group. So if your group is of order 20, it must be one of (Z_20), (Z_10)x(Z_2), (Z_5)x(Z_4), (Z_5)x(Z_2)x(Z_2). But (Z_mn)=(Z_M)x(Z_n) iff m,n are coprime. So (Z_20) is isomorphic to (Z_5)x(Z_4). (Z_4) is not iso to (Z_2)x(Z_2) because 2 and 2 are not coprime. Also, (Z_20) is not ...

Source: Physics Help and Math Help - Physics Forums

Forum: Linear & Abstract Algebra

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Abelian groups of order 70 are cyclic

Started 3 weeks, 6 days ago (2009-11-14 15:32:00) by redone632

1. The problem statement, all variables and given/known data Show that every abelian group of order 70 is cyclic. 2. Relevant equations Cannot use the Fundamental Theorem of Finite Abelian Groups. 3. The attempt at a solution I've tried to prove the contrapositive and suppose that it is not cyclic then it cannot be abelian. But that has lead no ...

Source: Physics Help and Math Help - Physics Forums

Forum: Calculus & Beyond

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Re: Abelian groups of order 70 are cyclic

Started 3 weeks, 5 days ago (2009-11-15 15:59:00) by Quantumpencil

There are two groups of order 21, even though it's isomorphic to the direct product of the Cyclic Group of Order 3 and the Cyclic Group of order 7. 3 and 7 are co-prime. EDIT: Nevermind, didn't read the "abelian" in the problem. Your proof is good.

Source: Physics Help and Math Help - Physics Forums

Forum: Calculus & Beyond

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Proving that abelian groups are free iff projective

Started 1 month, 2 weeks ago (2009-10-25 10:36:00) by arcoraven

How would I prove that an abelian group is free abelian if and only if it has the projective property? I'm lost and don't know where to begin. If anyone could help that'd be great. Thanks!

Source: Math Forum :: Index

Forum: Algebra: groups, rings, fields, modules, Galois Th...

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Re: Proving that abelian groups are free iff projective

Started 1 month ago (2009-11-11 09:26:00) by zolden

Elements of the free abelian group are distinguished only by its components - generator elements. That are form a basis, that, in turn, gives projective property. Otherwise, projective property gives a basis, that makes group abelian.

Source: Math Forum :: Index

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