Department or Administrative Unit
Let G=〈X〉be an absolutely irreducible subgroup of GL(d, K), and let F be a proper subfield of the finite field K. We present a practical algorithm to decide constructively whether or not G is conjugate to a subgroup of GL(d, F).K×, where K× denotes the centre of GL(d, K). If the derived group of G also acts absolutely irreducibly, then the algorithm is Las Vegas and costs O(|X|d3+d2log|F|) arithmetic operations in K. This work forms part of a recognition project based on Aschbacher’s classification of maximal subgroups of GL(d, K).
Glasby, Stephen P.; Leedham-Green, C. R.; and O'Brien, E. A., "Writing projective representations over subfields" (2006). All Faculty Scholarship for the College of the Sciences. 238.
Journal of Algebra
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