Leírás
Abstract:
Let FG be the group ring of a non-abelian group G over a field F of characteristic p>0. A classical problem of interest in the study of group rings is to classify the groups G such that the unit group, U(FG), of FG satisfies certain identities. In this direction, the conditions under which U(FG) is solvable were determined in a series of papers over many years, the final result was given by A. Bovdi in 2005. On the assumption that U(FG) is solvable, it is natural to ask about its derived length, but the picture is not as clear here. One of the first results was due to A. Shalev in 1991, who classified the finite groups G such that U(FG) is metabelian, when p is odd. Namely he proved that this occurs if, and only if, p=3 and the commutator subgroup of G is central of order 3. In this presentation we are going to take this 30-year-old theorem and look at what happens without the restriction that G is finite.
This joint research with E. Spinelli was partially supported by the National Research, Development and Innovation Office (NKFIH) Grant No. K132951.
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