Abstract
G-character tables of a finite group G were defined in Felipe et al. (Quaest Math, 2022. https://doi.org/10.2989/16073606/16073606.2022.2040633). These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal subgroups which can be determined using their G-character tables. For instance, we prove an extension of the Thompson’s theorem from minimal G-invariant characters of a normal subgroup. We also obtain a variation of Taketa’s theorem for hypercentral normal subgroups considering their minimal G-invariant characters. This generalization allows us to introduce a new class of nilpotent groups, the class of nMI-groups, whose members verify that its nilpotency class is bounded by the number of irreducible character degrees of the group.
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Acknowledgements
The authors would like to thank the referee for his or her comments which led to the improvement of this work. This work was done during a visit of the first author at Universitat Politècnica de València(UPV) and Universitat de València(UV). She wishes to thank them for their hospitality. The results in this paper are part of the third author’s Ph.D. thesis, and he acknowledges the support of Instituto Tecnológico de Santo Domingo (INTEC) and Universidad Autónoma de Santo Domingo (UASD), Santo Domingo, (Dominican Republic).
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Communicated by Peyman Niroomand.
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The first author is supported by a grant from IPM (No. 1402200112) and the second author is supported by Proyecto CIAICO/2021/163, Generalitat Valenciana (Spain).
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Akhlaghi, Z., Felipe, M.J. & Jean-Philippe, M.K. Some Properties of Normal Subgroups Determined from Character Tables. Bull. Malays. Math. Sci. Soc. 47, 90 (2024). https://doi.org/10.1007/s40840-024-01684-6
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DOI: https://doi.org/10.1007/s40840-024-01684-6
Keywords
- Finite groups
- Irreducible characters
- Normal subgroups
- Minimal G-invariant characters
- Hypercentral subgroup