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arXiv · 1310.5454

The minimal base size for a p-solvable linear group

Zoltán Halasi·Attila Maróti
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Abstract

Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$. Let $G\leq GL(V)$ be a $p$-solvable completely reducible linear group. Then there exists a base for $G$ on $V$ of size at most $2$ unless $q \leq 4$ in which case there exists a base of size at most $3$. The first statement extends a recent result of Halasi and Podoski and the second statement generalizes a theorem of Seress. An extension of a theorem of P\'alfy and Wolf is also given.

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Zoltán Halasi, Attila Maróti. 2013-10-21. The minimal base size for a p-solvable linear group. https://doi.org/10.1090/proc%2F12974

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