Regular orbits of finite primitive solvable groups, III

2016/12/18 by Yang, Yong, Vasil'ev, Alexey, Vdovin, Evgeny · 1 citation
#20C15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1612.05959

Abstract

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V. Then G has a uniquely determined normal subgroup E which is a direct product of extraspecial p-groups for various p and we denote e=√(|E/\bZ(E)|). We prove that when e=2,3,4,8,9,16, G will have regular orbits on V when the corresponding vector space is not too small.

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