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A note on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups
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Masahiko Miyamoto
Published/Copyright:
November 20, 2009
Abstract
For a p-block B of a finite group G, it is well known that Σχi ∈ Bχi(1)χi vanishes on all p-singular elements of G. The converse proposition was proposed by K. Harada and partially proved by several authors using decomposition matrices. We give a partial answer without using decomposition matrices in the case where G has a strongly p-embedded subgroup.
Received: 2008-09-04
Revised: 2009-07-27
Published Online: 2009-11-20
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
