Above Isaacs' Head Characters
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910021462261760 |
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| author | Arranz, Asier |
| author_facet | Arranz, Asier |
| contents | The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the Isaacs' head characters of a normal solvable subgroup of an arbitrary group. In particular, we give a new lower bound of the number of conjugacy classes of a finite group in terms of the Carter subgroups of any of its normal solvable subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Above Isaacs' Head Characters Arranz, Asier Group Theory Representation Theory 20C15 (Primary) 20D10 (Secondary) The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the Isaacs' head characters of a normal solvable subgroup of an arbitrary group. In particular, we give a new lower bound of the number of conjugacy classes of a finite group in terms of the Carter subgroups of any of its normal solvable subgroups. |
| title | Above Isaacs' Head Characters |
| topic | Group Theory Representation Theory 20C15 (Primary) 20D10 (Secondary) |
| url | https://arxiv.org/abs/2602.12849 |