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arXiv · 2002.00648

On element orders in covers of $L_4(q)$ and $U_4(q)$

Mariya A. Grechkoseeva·Saveliy V. Skresanov
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Abstract

Suppose that $L$ is one of the finite simple groups $PSL_4(q)$ or $PSU_4(q)$ and $L$ acts on a vector space $W$ over a field whose characteristic divides $q$. We prove that the natural semidirect product of $W$ and $L$ contains an element whose order differs from the order of any element of $L$, thus answering questions 14.60 and 17.73 (a) of the Kourovka Notebook.

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Mariya A. Grechkoseeva, Saveliy V. Skresanov. 2020-02-03. On element orders in covers of $L_4(q)$ and $U_4(q)$. https://doi.org/10.33048/semi.2020.17.037

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