On sharp characters of type $\{-1,0,2\}$

Abdollahi, Alireza, et al. "On sharp characters of type $\lbrace -1,0,2 \rbrace $." Czechoslovak Mathematical Journal 72.4 (2022): 1081-1087. <http://eudml.org/doc/298914>.

@article{Abdollahi2022,
abstract = {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-\lbrace 1\rbrace $. 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 $\lbrace -1,0,2\rbrace $. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12.},
author = {Abdollahi, Alireza, Bagherian, Javad, Ebrahimi, Mahdi, Khatami, Maryam, Shahbazi, Zahra, Sobhani, Reza},
journal = {Czechoslovak Mathematical Journal},
keywords = {sharp character; sharp pair; finite group},
language = {eng},
number = {4},
pages = {1081-1087},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On sharp characters of type $\lbrace -1,0,2 \rbrace $},
url = {http://eudml.org/doc/298914},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Abdollahi, Alireza
AU - Bagherian, Javad
AU - Ebrahimi, Mahdi
AU - Khatami, Maryam
AU - Shahbazi, Zahra
AU - Sobhani, Reza
TI - On sharp characters of type $\lbrace -1,0,2 \rbrace $
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1081
EP - 1087
AB - 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-\lbrace 1\rbrace $. 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 $\lbrace -1,0,2\rbrace $. Here we prove that such a group with nontrivial center is isomorphic to the dihedral group of order 12.
LA - eng
KW - sharp character; sharp pair; finite group
UR - http://eudml.org/doc/298914
ER -