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arXiv · 1612.05959

Regular orbits of finite primitive solvable groups, III

Yong Yang·Alexey Vasil'ev·Evgeny Vdovin
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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 $e=\sqrt{|E/\bZ(E)|}$. 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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Yong Yang, Alexey Vasil'ev, Evgeny Vdovin. 2016-12-18. Regular orbits of finite primitive solvable groups, III. https://arxiv.org/abs/1612.05959

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