57 245
Assignments Done
Successfully Done
In February 2018
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Abstract Algebra Question for john.george.milnor

Question #23730
For finite abelian groups G and H, show that RG ∼ RH as R-algebras iff |G| = |H| and |G/G2| = |H/H2|.
Expert's answer
Since G is abelian, Wedderburn’s Theoremgives: RG ∼ R×· ··×R × C×· · ·×C.Suppose there are s factors ofR, and t factors of C, so that |G| = s + 2t. Thenumber s is the number of 1-dimensional real representations of G.This is the number of group homomorphisms from G to {±1} ⊆R*, so s = |G/G2|. Therefore, the isomorphism typeof RG (as an R-algebra) is uniquely determined by |G| and |G/G2|.The conclusion follows immediately from this.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question