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Let $\pi$ be a finite group of odd order. What do we know about the torsion subgroup of $Wh(\pi)$? I am especially interested in the $2$-primary part. Is it always trivial?

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    $\begingroup$ I would start with Bob Oliver's Whitehead groups of finite groups. LMS Lecture Note Series, 132. Cambridge University Press, Cambridge, 1988. It's complicated and technical, but there are a bunch of examples computed in the last section that might answer your question. $\endgroup$
    – Danny Ruberman
    Commented Jul 24, 2013 at 1:52

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