Abstract
Considering the groups \( PSL_{3}(2^{m}) \) and \( PSU_{3}(q^{2}) \), we find the minimal number of generating involutions whose product is 1. This number is 7 for \( PSU_{3}(3^{2}) \) and 5 or 6 in the remaining cases.
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Acknowledgment
We thank A.V. Timofeenko for his lectures on the GAP system in the fall of 2022 at Siberian Federal University and the Krasnoyarsk Mathematical Center for organizing this lecture course.
Funding
The research was supported by the Russian Science Foundation (Grant no. 22–21–00733).
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 6, pp. 1160–1171. https://doi.org/10.33048/smzh.2023.64.605
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Gvozdev, R.I., Nuzhin, Y.N. The Minimal Number of Generating Involutions Whose Product Is 1 for the Groups \( PSL_{3}(2^{m}) \) and \( PSU_{3}(q^{2}) \). Sib Math J 64, 1297–1306 (2023). https://doi.org/10.1134/S0037446623060058
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DOI: https://doi.org/10.1134/S0037446623060058
Keywords
- finite simple group
- generating set of involutions
- character of a group representation
- special linear and unitary groups