Abstract
We define weakly quasi-primitive characters of solvable groups as a generalization of quasi-primitive characters, and present three main results about the zeros and the values for these characters, which in turn strengthen the corresponding theorems for quasi-primitive characters due to G. Navarro and T. Wilde.
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Isaacs, I.M.: Characters of solvable and symplectic groups. Am. J. Math. 95, 594–635 (1973)
Isaacs, I.M.: Character Theory of Finite Groups. Academic Press, New York (1976)
Isaacs, I.M.: Characters of \(\pi \)-separable groups. J. Algebra 86, 98–128 (1984)
Isaacs, I.M.: Fong characters in \(\pi \)-separable groups. J. Algebra 99, 89–107 (1986)
Isaacs, I.M.: Partial characters of \(\pi \)-separable groups. In: Michler, G.O., Ringel, C.M. (eds.) Progress in Mathematics, vol. 95, pp. 273–287. Birkhäuser Verlag, Basel (1991)
Navarro, G.: Characters and Blocks of Finite Groups. Cambridge University Press, Cambridge (1998)
Navarro, G.: Zeros of primitive characters in solvable groups. J. Algebra 221, 644–650 (1999)
Navarro, G.: Induction of characters and \(p\)-subgroups. J. Algebra 221, 217–228 (2002)
Wilde, T.: Primitive characters and permutation characters of solvable groups, preprint (2008). arXiv:0709.1209v2
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The second author was supported by the NSF of China (No. 11671238) and the NSF of Shanxi Province (No. 201601D011006).
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Chang, H., Jin, P. On weakly quasi-primitive characters of solvable groups. Arch. Math. 111, 561–568 (2018). https://doi.org/10.1007/s00013-018-1212-y
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DOI: https://doi.org/10.1007/s00013-018-1212-y