The derived length of the unit group of a group algebra - The case G ' = Syl(p) (G)

摘要

Let p be an odd prime, and let G be a nilpotent group, whose commutator subgroup is finite abelian satisfying G' = Syl(p)(G) and gamma(3)(G) subset of (G')(p). In this contribution, an upper bound is given on the derived length of the group of units of the group algebra of G over a field of characteristic p. Furthermore, we show that this bound is achieved, whenever G' is cyclic.