Every coprime linear group admits a base of size two

Halasi, Zoltán; Podoski, Károly

doi:10.1090/tran/6544

Every coprime linear group admits a base of size two
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by Zoltán Halasi and Károly Podoski PDF

Trans. Amer. Math. Soc. 368 (2016), 5857-5887 Request permission

Abstract:

Let $G$ be a linear group acting faithfully on a finite vector space $V$ and assume that $(|G|,|V|) =1$. In this paper we prove that $G$ admits a base of size two and that this estimate is sharp. This generalizes and strengthens several former results concerning base sizes of coprime linear groups. As a direct consequence, we answer a question of I. M. Isaacs in the affirmative.

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