“School of Mathematics”
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Paper IPM / M / 17795  


Abstract:  
Gcharacter 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 Gcharacter tables. For instance, we prove an extension of the Thompsonâs theorem from minimal Ginvariant characters of a normal subgroup. We also obtain a variation of Taketaâs theorem for hypercentral normal subgroups considering their minimal Ginvariant characters. This generalization allows us to introduce a new class of nilpotent groups, the class of nMIgroups, whose members verify that its nilpotency class is bounded by the number of irreducible character degrees of the group.
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