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Abstract
Let KG be a non-commutative group algebra of a torsion nilpotent group G over a field K of positive characteristic p whose unit group, 𝒰(KG), is solvable. In the present note we prove that dl(𝒰(KG)) ⩾ ⌈log2(p + 1)⌉ and characterize group algebras for which this lower bound is achieved.
Received: 2009-06-17
Revised: 2009-10-19
Published Online: 2010-02-08
Published in Print: 2010-July
© de Gruyter 2010