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On a generalization of M-group

arXiv:1206.5067 · doi:10.1016/j.jalgebra.2012.10.018

Abstract

In this paper, we will show that if for every nonlinear complex irreducible character of a finite group G, some multiple of it is induced from an irreducible character of some proper subgroup of G, then G is solvable. This is a generalization of Taketa's Theorem on the solvability of M-group.

17 pages, to appear in J. Algebra