Geodesic
Regular orbits of solvable linear $p'$-groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 345-360

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In this paper we prove that a solvable linear $p'$-group $G\le GL(V)$, where $p$ is the characteristic of the underlying field of $V$, has a regular orbit on $V\times V$. 
@article{SEMR_2007_4_a21,
     author = {E. P. Vdovin},
     title = {Regular orbits of solvable linear $p'$-groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {345--360},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a21/}
}
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E. P. Vdovin. Regular orbits of solvable linear $p'$-groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 345-360. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a21/