| Title:
|
On zeros of characters of finite groups (English) |
| Author:
|
Zhang, Jinshan |
| Author:
|
Shen, Zhencai |
| Author:
|
Liu, Dandan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
801-816 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a finite group $G$ and a non-linear irreducible complex character $\chi $ of $G$ write $\upsilon (\chi )=\{g\in G\mid \chi (g)=0\}$. In this paper, we study the finite non-solvable groups $G$ such that $\upsilon (\chi )$ consists of at most two conjugacy classes for all but one of the non-linear irreducible characters $\chi $ of $G$. In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question and are called solvable $\varphi $-groups. As a corollary, we answer Research Problem $2$ in [Y. Berkovich and L. Kazarin: Finite groups in which the zeros of every non-linear irreducible character are conjugate modulo its kernel. Houston J. Math.\ 24 (1998), 619--630.] posed by Y. Berkovich and L. Kazarin. (English) |
| Keyword:
|
finite groups |
| Keyword:
|
characters |
| Keyword:
|
zeros |
| MSC:
|
20C15 |
| idZBL:
|
Zbl 1208.20005 |
| idMR:
|
MR2672416 |
| . |
| Date available:
|
2010-07-20T17:20:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140605 |
| . |
| Reference:
|
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