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## Quantitative characterization of finite simple groups: a complement | ||

International Journal of Group Theory | ||

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 شهریور 1403 اصل مقاله (606.45 K) | ||

نوع مقاله: Research Paper | ||

شناسه دیجیتال (DOI): 10.22108/ijgt.2024.140804.1893 | ||

نویسنده | ||

Wujie Shi^{*}
| ||

^{}School of Mathematical Sciences, Suzhou University, Suzhou, Jiangsu, P. R.China | ||

چکیده | ||

In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with ``the set of element orders" and ``two orders" (the order of group and the set of element orders). Some related topics, and the applications together with their generalizations are also discussed. The original version of this article was published in Chinese in the journal Scientia Sinica Mathematica, no.53 (2023) 931-952. This revised and expanded version has corrected several errors and added quite a few contents. Especially, it is pointed that this work has applications in mathematics and computational complexity theory. | ||

کلیدواژهها | ||

Finite group؛ Group orders؛ Element orders؛ Classification theorem for finite simple groups | ||

مراجع | ||

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