Geodesic
Exceptional action of the simple groups $L_4(q)$ in the defining characteristic
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 68-74

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We find a counterexample to Problem 14.60 from the Kourovka notebook by giving an example of a group $\rm {PSL}_4(q)$ which is not recognizable among its covers from spectrum. Namely, we show that such a group has a module in the defining characteristic with the property that the element order set of the corresponding semidirect product equals that of the group itself. 
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     author = {A. V. Zavarnitsine},
     title = {Exceptional action of the simple groups $L_4(q)$ in the defining characteristic},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {68--74},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a7/}
}
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A. V. Zavarnitsine. Exceptional action of the simple groups $L_4(q)$ in the defining characteristic. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 68-74. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a7/