On the degrees of irreducible characters fixed by some field automorphism, p-solvable groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929208971755520 |
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| author | Grittini, Nicola |
| author_facet | Grittini, Nicola |
| contents | It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the group to be $p$-solvable. In particular, it is proved that a $p$-solvable group has a normal Sylow $p$-subgroup if $p$ does not divide the degree of any irreducible character of the group fixed by a field automorphism of order $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_03804 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the degrees of irreducible characters fixed by some field automorphism, p-solvable groups Grittini, Nicola Group Theory 20C15 It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the group to be $p$-solvable. In particular, it is proved that a $p$-solvable group has a normal Sylow $p$-subgroup if $p$ does not divide the degree of any irreducible character of the group fixed by a field automorphism of order $p$. |
| title | On the degrees of irreducible characters fixed by some field automorphism, p-solvable groups |
| topic | Group Theory 20C15 |
| url | https://arxiv.org/abs/2011.03804 |