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Solvability of generalized monomial groups
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Joachim König
Published/Copyright:
August 31, 2009
Abstract
The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to groups with the property that every irreducible character has some multiple which is induced from a character φ of U with solvable factor group U/ker(φ). Using the classification of finite simple groups, we prove that these groups are also solvable. This means in particular that the mentioned properties do not enable one to deduce a proof of the famous Artin conjecture for any non-solvable group from a possible proof for solvable groups.
Received: 2009-01-21
Revised: 2009-06-16
Published Online: 2009-08-31
Published in Print: 2010-March
© de Gruyter 2010
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- Zeros of Brauer characters and the defect zero graph
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- Solvability of generalized monomial groups
- Group algebras of torsion groups and Lie nilpotence
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Articles in the same Issue
- Class numbers of group extensions
- Zeros of Brauer characters and the defect zero graph
- On the vanishing prime graph of solvable groups
- Solvability of generalized monomial groups
- Group algebras of torsion groups and Lie nilpotence
- An axiomatic formation that is not a variety
- Minimal odd order automorphism groups
- Finite groups with normally embedded subgroups
- The influence of ℋ-subgroups on the structure of finite groups
- Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane
- On ω-categorical groups and their completions
