Uniformly semi-rational groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913915843117056 |
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| author | del Río, Ángel Vergani, Marco |
| author_facet | del Río, Ángel Vergani, Marco |
| contents | We introduce and study some families of groups whose irreducible characters take values on quadratic extensions of the rationals. We focus mostly on a generalization of inverse semi-rational groups, which we call uniformly semi-rational groups. Moreover, we associate to every finite group two invariants, called rationality and semi-rationality of the group. They measure respectively how far a group is from being rational and how much uniformly rational it is. We determine the possible values that these invariants may take for finite nilpotent groups. We also classify the fields that can occur as the field generated by the character values of a finite nilpotent group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformly semi-rational groups del Río, Ángel Vergani, Marco Group Theory Representation Theory We introduce and study some families of groups whose irreducible characters take values on quadratic extensions of the rationals. We focus mostly on a generalization of inverse semi-rational groups, which we call uniformly semi-rational groups. Moreover, we associate to every finite group two invariants, called rationality and semi-rationality of the group. They measure respectively how far a group is from being rational and how much uniformly rational it is. We determine the possible values that these invariants may take for finite nilpotent groups. We also classify the fields that can occur as the field generated by the character values of a finite nilpotent group. |
| title | Uniformly semi-rational groups |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2411.16563 |