Journal of the Ramanujan Mathematical Society

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Finite Order Elements in the Integral Symplectic Group


Affiliations
1 Department of Mathematics, IISER Bhopal, Bhopal, Madhya Pradesh 462066, India
2 Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, India
     

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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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  • Finite Order Elements in the Integral Symplectic Group

Abstract Views: 251  |  PDF Views: 1

Authors

Kumar Balasubramanian
Department of Mathematics, IISER Bhopal, Bhopal, Madhya Pradesh 462066, India
M. RamMurty
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, India
Karam Deo Shankhadhar
Department of Mathematics, IISER Bhopal, Bhopal, Madhya Pradesh 462066, India

Abstract


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.

References