arXiv 0901.34412009-01-22math.GR

Solvability of Generalized Monomial Groups

Joachim König

备注：: 21 pages
发表信息：: Journal of Group Theory 13 (2010), 207-220

英文摘要：

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 such groups where every irreducible character has some multiple which is induced from a character phi of U with solvable factor group U/ker(phi). 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.

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