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On the derived length of the unit group of a group algebra
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Francesco Catino
Published/Copyright:
February 8, 2010
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
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Articles in the same Issue
- A note on the Green theory in the Clifford-theoretic context of a defect zero p-block of a normal subgroup of a finite group
- A note on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups
- Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules
- Some linear actions of finite groups with q′-orbits
- Semi-rational solvable groups
- Finite non-abelian 2-groups such that any two distinct minimal non-abelian subgroups have cyclic intersection
- A note on the p-supersolvability of finite groups
- Vertex-transitive tournaments of order a product of two distinct primes
- On the derived length of the unit group of a group algebra
- On the subgroups with non-trivial Möbius number
- Subgroups of free groups and primitive elements
- Small index subgroups of the mapping class group
