Solvable groups whose monomial, monolithic characters have prime power codegrees
In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2023-12-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | https://ijgt.ui.ac.ir/article_26289_47bc384bead7c28b76c6eff6dc178c60.pdf |
| _version_ | 1797988576953106432 |
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| author | Xiaoyou Chen Mark Lewis |
| author_facet | Xiaoyou Chen Mark Lewis |
| author_sort | Xiaoyou Chen |
| collection | DOAJ |
| description | In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $G$. |
| first_indexed | 2024-04-11T08:06:21Z |
| format | Article |
| id | doaj.art-b4870342a3ee4101878348a1ad1b7845 |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-04-11T08:06:21Z |
| publishDate | 2023-12-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-b4870342a3ee4101878348a1ad1b78452022-12-22T04:35:34ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692023-12-0112422322610.22108/ijgt.2022.131101.175526289Solvable groups whose monomial, monolithic characters have prime power codegreesXiaoyou Chen0Mark Lewis1School of Sciences, Henan University of Technology, P.O.Box 450001, Zhengzhou, ChinaDepartment of Mathematical Sciences, Kent State University, P.O.Box 44242, Kent, USAIn this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $G$.https://ijgt.ui.ac.ir/article_26289_47bc384bead7c28b76c6eff6dc178c60.pdfmonomial charactersmonolithic characterscharacter codegrees |
| spellingShingle | Xiaoyou Chen Mark Lewis Solvable groups whose monomial, monolithic characters have prime power codegrees International Journal of Group Theory monomial characters monolithic characters character codegrees |
| title | Solvable groups whose monomial, monolithic characters have prime power codegrees |
| title_full | Solvable groups whose monomial, monolithic characters have prime power codegrees |
| title_fullStr | Solvable groups whose monomial, monolithic characters have prime power codegrees |
| title_full_unstemmed | Solvable groups whose monomial, monolithic characters have prime power codegrees |
| title_short | Solvable groups whose monomial, monolithic characters have prime power codegrees |
| title_sort | solvable groups whose monomial monolithic characters have prime power codegrees |
| topic | monomial characters monolithic characters character codegrees |
| url | https://ijgt.ui.ac.ir/article_26289_47bc384bead7c28b76c6eff6dc178c60.pdf |
| work_keys_str_mv | AT xiaoyouchen solvablegroupswhosemonomialmonolithiccharactershaveprimepowercodegrees AT marklewis solvablegroupswhosemonomialmonolithiccharactershaveprimepowercodegrees |