The integral group ring of a polycyclic-by-finite group was shown to be Noetherian by Philip Hall. Are there any other known examples?
1 Answer
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As far as I know the only groups known to have a Noetherian integral group ring are polycyclic-by-finite groups. This is often discussed in connection with the so-called "Zero Divisor Conjecture" for amenable groups of finite cohomological dimension, whose integral group ring is noetherian, e.g., see here (in particular, page $5$).