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- W2037797410 abstract "In this paper we introduce and study a family (mathcal{A}_{n}(q)) of abelian subgroups of ({rm GL}_{n}(q)) covering every element of ({rm GL}_{n}(q)). We show that (mathcal{A}_{n}(q)) contains all the centralizers of cyclic matrices and equality holds if q>n. For q>2, we obtain an infinite product expression for a probabilistic generating function for (|mathcal{A}_{n}(q)|). This leads to upper and lower bounds which show in particular that $$c_1q^{-n}leq frac{|mathcal{A}_n(q)|}{|mathrm{GL}_n(q)|}leq c_2q^{-n}$$for explicit positive constants c1,c2. We also prove that similar upper and lower bounds hold for q=2." @default.
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- W2037797410 date "2011-04-29" @default.
- W2037797410 modified "2023-09-24" @default.
- W2037797410 title "Abelian coverings of finite general linear groups and an application to their non-commuting graphs" @default.
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- W2037797410 doi "https://doi.org/10.1007/s10801-011-0288-2" @default.
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