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The integral group ring of a polycyclic-by-finite group was shown to be Noetherian by Philip Hall. Are there any other known examples?

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  • $\begingroup$ This very question was addressed here mathoverflow.net/a/165065/14094 in this generality (although the question was more of a particular case). $\endgroup$
    – YCor
    Oct 15, 2020 at 21:36

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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 $5$).

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