Timeline for Algorithm to calculate $Wh(G)$ for finitely presented group $G$?

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Jun 23, 2011 at 15:43	comment	added	user6976		Igor: You are right, the proof is harder than I thought (I thought that zero divisors somewhow produce non-trivial elements in Wh). The reference you give below uses both the Adyan-Rabin theorem and its proof.
Jun 23, 2011 at 13:19	comment	added	Igor Belegradek		I checked, and indeed, $S_n$ does have trivial Whitehead group for any $n$. This can be found e.g in Oliver's book "Whitehead groups of finite groups", Theorem 14.1, also mentioned in example 4 on page 14, which can be viewed in google books.
Jun 23, 2011 at 12:32	comment	added	Igor Belegradek		Mark, if I understand your argument correctly, it asserts that if a group $G$ has zero Whitehead group, then $G$ is torsion-free. This is not true. For example, $\mathbb Z_2$ has trivial Whitehead group, and if memory serves me, so does $S_n$.
Jun 23, 2011 at 8:49	history	edited	user6976	CC BY-SA 3.0	added 304 characters in body
Jun 23, 2011 at 8:39	comment	added	user6976		See reference [6] in eom.springer.de/a/a011860.htm
Jun 23, 2011 at 8:31	comment	added	Wilberd van der Kallen		Can you explain why the Markov property implies there is no algorithm? Maybe by a reference.
Jun 23, 2011 at 7:48	history	edited	user6976	CC BY-SA 3.0	added 2 characters in body
Jun 23, 2011 at 7:33	history	answered	user6976	CC BY-SA 3.0