| Title:
|
On sharp characters of type $\{ -1,0,2 \}$ (English) |
| Author:
|
Abdollahi, Alireza |
| Author:
|
Bagherian, Javad |
| Author:
|
Ebrahimi, Mahdi |
| Author:
|
Khatami, Maryam |
| Author:
|
Shahbazi, Zahra |
| Author:
|
Sobhani, Reza |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
1081-1087 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a complex character $ \chi $ of a finite group $ G $, it is known that the product $ {\rm sh}(\chi ) = \prod _{ l \in L(\chi )} (\chi (1) - l) $ is a multiple of $ |G| $, where $ L(\chi ) $ is the image of $ \chi $ on $ G-\{1\}$. The character $ \chi $ is said to be a sharp character of type $ L $ if $ L=L(\chi ) $ and $ {\rm sh} (\chi )=|G| $. If the principal character of $G$ is not an irreducible constituent of $\chi $, then the character $\chi $ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups $G$ with normalized sharp characters of type $\{-1,0,2\}$. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12. (English) |
| Keyword:
|
sharp character |
| Keyword:
|
sharp pair |
| Keyword:
|
finite group |
| MSC:
|
20C15 |
| idZBL:
|
Zbl 07655784 |
| idMR:
|
MR4517597 |
| DOI:
|
10.21136/CMJ.2022.0356-21 |
| . |
| Date available:
|
2022-11-28T11:38:05Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151131 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
