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Research articles

ScienceAsia 45 (2019): 474-481 |doi: 10.2306/scienceasia1513-1874.2019.45.474

On groups with consecutive three smallest character degrees

Shitian Liua,*, Donglin Leib, Xianhua Lib

ABSTRACT:     Huppert determined the structure of groups whose degrees are consecutive, then Qian improved that Huppert’s result and showed the structure of finite groups whose degrees of nonlinear characters are consecutive. In this paper, we considered the case when the first three smallest degrees of nonlinear irreducible characters of an almost simple group G are consecutive. Furthermore, Huppert’s conjecture is proved valid for those groups.

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a School of Science, Sichuan University of Science and Engineeing, Zigong Sichuan 643000 China
b School of Mathematical Science, Soochow University, Suzhou, Jiangsu 251125 China

* Corresponding author, E-mail: s.t.liu@yandex.com

Received 13 Aug 2018, Accepted 4 Sep 2019