Glasnik Matematicki, Vol. 49, No. 1 (2014), 83-103.

FINITE GROUPS WITH FEW VANISHING ELEMENTS

Jinshan Zhang, Zhencai Shen and Jiangtao Shi

School of Science, Sichuan University of Science and Engineering, 643000 Zigong, P. R. China
e-mail: zjscdut@163.com

College of Science, China Agricultural University, 100083 Beijing, P. R. China
e-mail: zhencai688@sina.com

School of Mathematics and Information Science, Yantai University, 264005 Yantai, P. R. China
e-mail: shijt@math.pku.edu.cn


Abstract.   Let G be a finite group, and Irr(G) the set of irreducible complex characters of G. We say that an element g G is a vanishing element of G if there exists χ in Irr(G) such that χ(g)= 0. Let Van(G) denote the set of vanishing elements of G, that is, Van(G)= {g G|χ(g)=0 for some χ Irr (G)}. In this paper, we investigate the finite groups G with the following property: Van(G) contains at most four conjugacy classes of G.

2010 Mathematics Subject Classification.   20C15.

Key words and phrases.   Finite groups, characters, vanishing elements.


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DOI: 10.3336/gm.49.1.07


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