“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 17795 |
|
| 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 Thompsonâs theorem from minimal G-invariant characters of a normal subgroup. We also obtain a variation of Taketaâs 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.
Download TeX format |
|
| back to top | |
