Generalizing a theorem of Gagola and Lewis characterizing nilpotent groups |
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Authors: | Jiakuan Lu Xueqing Qin Xuexia Liu |
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Institution: | 1.School of Mathematics and Statistics,Guangxi Normal University,Guilin,People’s Republic of China |
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Abstract: | Gagola and Lewis proved that a finite group G is nilpotent if and only if \(\chi (1)^2\) divides |G : \(\mathrm{Ker}\) \(\chi |\) for all irreducible characters \(\chi \) of G. In this paper, we prove the following generalization that a finite group G is nilpotent if and only if \(\chi (1)^2\) divides |G : \(\mathrm{Ker}\) \(\chi |\) for all monolithic characters \(\chi \) of G. |
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