On a generalization of M-group

doi:10.1016/j.jalgebra.2012.10.018

Journal of Algebra

Volume 374, 15 January 2013, Pages 27-41

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Abstract

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

MSC

primary

20C15

secondary

20D10

20D05

20C33

Keywords

M-groups

Multiply imprimitive characters

Solvable groups

Cited by (0)

¹: Alternative international address: Viet Nam National University, Ho Chi Minh City, Viet Nam.

²: Supported by North-West University (Mafikeng) and the NAFOSTED (Viet Nam).

³: Supported by North-West University (Mafikeng) and a Competitive Grant from NRF.

⁴: Supported by NRF and North-West University (Mafikeng).