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Finite Order Elements in the Integral Symplectic Group
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For g ∈ ℕ, let G = Sp(2g, ℤ) be the integral symplectic group and S(g) be the set of all positive integers which can occur as the order of an element in G. In this paper, we show that S(g) is a bounded subset of ℝ for all positive integers g. We also study the growth of the functions f (g) = |S(g)|, and h(g) = max{m ∈ ℕ | m ∈ S(g)} and show that they have at least exponential growth.
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