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Is there a good reference for studying the ideal structure of group C* algebras? Thanks.

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Another way to state this condition is that every subgroup $H<G$ has commensurator $\text{Comm}_G(H)$ equal to all of $G$. The commensurator in $G$ of a subgroup $H$ consists of all those $g$ for which $H\cap gHg^{-1}$ has finite index in $H$ and in $gHg^{-1}$.) (Note that in your question you need to intersect $H$ with $gHg^{-1}$ to ensure you get a subgroup of $H$.) Do you have examples of not-virtually-solvable groups for which this condition holds? –  Tom Church May 31 '10 at 18:57
    
A classic is Pedersen's book, unfortunately not readable here: books.google.com/books?id=yBCoAAAAIAAJ –  Steve Huntsman May 31 '10 at 19:18
    
Pedersen's book is available here in electronic form: gen.lib.rus.ec/get?md5=D0251C94AFFF04ECBD38BDC97F51AF2D –  Dmitri Pavlov May 31 '10 at 19:25
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I think it is a bad idea to completely replace a question like this, in particular because Tom Church spent time writing a comment for the original question. If you figured out the first question as it says in the edit history, you could post the answer. –  Jonas Meyer May 31 '10 at 19:36
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