Abstract
Let be a vector space of dimension over , a finite field of elements, and let be a linear group. A base for is a set of vectors whose pointwise stabilizer in is trivial. We prove that if is a quasisimple group (i.e., is perfect and is simple) acting irreducibly on , then excluding two natural families, has a base of size at most 6. The two families consist of alternating groups acting on the natural module of dimension or , and classical groups with natural module of dimension over subfields of .
Citation
Melissa Lee. Martin W. Liebeck. "Bases for quasisimple linear groups." Algebra Number Theory 12 (6) 1537 - 1557, 2018. https://doi.org/10.2140/ant.2018.12.1537
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