Re: skew fields

From: William C Waterhouse (wcw_at_math.psu.edu)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 22:30:03 +0000 (UTC)

In article <d1mtmd$3hh$1@dizzy.math.ohio-state.edu>,
"Pete" <pete_muller78@hotmail.com> writes:
>
> Is it known if the multiplicative group of a skew field is residually
> finite?
> Any references are welcome.
> Pete
>

If I understaned the summary correctly, the following paper
should supply a counterexample (information taken from MathSciNet):

    Kegel, Otto H, Zur Einfachheit der multiplikativen Gruppe eines
  existentiell abgeschlossenen Schiefkoerpers. (German. English summary)
  [On the simplicity of the multiplicative group of an existentially
  closed skew field]
     Results Math. 35 (1999), no. 1-2, 103--106.

Summary: "Let $E$ be an existentially closed skew field in the class of all
skew fields with given central subfield $Z$. For the multiplicative
group $E^*$ it is shown that the group $G\coloneq E^*/Z^*$ is simple."

William C. Waterhouse
Penn State