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H. Meng, A. Ballester-Bolinches, and R. Esteban-Romero.
On large orbits of supersoluble subgroups of linear groups.
J. Lond. Math. Soc. (2), 101(2):490–504, 2020.
Abstract
We prove that if G is a finite soluble group, V is a finite faithful completely reducible G-module, and H is a supersoluble subgroup of G, then H has at least one regular orbit on V ⊕ V.
2020 Mathematics Subject Classification: 20C15, 20D10, 20D45
Keywords: linear group, regular orbit, supersoluble group