Groups whose vanishing class sizes are prime powers
| Autor: | Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Journal of Group Theory. 25:151-162 |
| ISSN: | 1435-4446 1433-5883 |
| Popis: | For a finite group 𝐺, an element is called a vanishing element of 𝐺 if it is a zero of an irreducible character of 𝐺; otherwise, it is called a non-vanishing element. Moreover, the conjugacy class of an element is called a vanishing class if that element is a vanishing element. In this paper, we describe finite groups whose vanishing class sizes are all prime powers, and on the other hand we show that non-vanishing elements of such a group lie in the Fitting subgroup which is a proof of a conjecture mentioned in [I. M. Isaacs, G. Navarro and T. R. Wolf, Finite group elements where no irreducible character vanishes, J. Algebra 222 (1999), 2, 413–423] under this special restriction on vanishing class sizes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|