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12.47 (1992)

Solved

Let $k$ be a field, let $p$ be a prime, and let $G$ be the Wreath product $\mathbb{Z}_p \wr \mathbb{Z}$ (so the base group has exponent $p$). Does $kG$ have a classical quotient ring? (i.e. do the non-zero-divisors of $kG$ form an Ore set?)

Contributor: P. A. Linnell

Progress

No, it does not (P. A. Linnell, W. Lück, T. Schick, in: High-dimensional manifold topology. Proc. of the school, ICTP (Trieste, 2001), World Scientific, River Edge, NJ, 2003, 315–321).

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