Geodesic
On element orders in covers of $L_4(q)$ and $U_4(q)$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 585-589

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Suppose that $L$ is one of the finite simple groups $\operatorname{PSL}_4(q)$ or $\operatorname{PSU}_4(q)$ 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.
Keywords: simple linear group, simple unitary group, orders of elements, modular representation, defining characteristic. 
@article{SEMR_2020_17_a9,
     author = {M. A. Grechkoseeva and S. V. Skresanov},
     title = {On element orders in covers of $L_4(q)$ and $U_4(q)$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {585--589},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a9/}
}
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M. A. Grechkoseeva; S. V. Skresanov. On element orders in covers of $L_4(q)$ and $U_4(q)$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 585-589. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a9/