Proportion of cyclic matrices in maximal reducible matrix algebras
Department or Administrative Unit
Let M(V)=M(n,Fq) denote the algebra of n×n matrices over Fq,and let M(V)U denote the (maximal reducible) subalgebra that normalizes a given r-dimensional subspace U of V=Fnq where 0U is at least q−2(1+c1q−1),and at most q−2(1+c2q−1),where c1 and c2 are constants independent of n, r, and q. The constants c1=−4/3 and c2=35/3 suffice.
Brown, S., Giudici, M., Glasby, S. P., & Praeger, C. E. (2012). Proportion of cyclic matrices in maximal reducible matrix algebras. Journal of Algebra, 369, 360–368. https://doi.org/10.1016/j.jalgebra.2012.06.024
Journal of Algebra
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