Abstract
The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive integer k, the k-th direct power of the simple linear group \(L_{n}(2)\) is uniquely determined by its spectrum in the class of finite groups provided n is a power of 2 greater than or equal to \(56k^2\).
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The first and fourth authors were supported by Foreign Experts program in Jiangsu Province (No. JSB2018014). The second, third, and fourth authors were supported by the Program of Fundamental Research RAS, project FWNF-2022-0002.
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Yang, N., Gorshkov, I., Staroletov, A. et al. On recognition of direct powers of finite simple linear groups by spectrum. Annali di Matematica 202, 2699–2714 (2023). https://doi.org/10.1007/s10231-023-01336-9
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DOI: https://doi.org/10.1007/s10231-023-01336-9