# Journal of the Ramanujan Mathematical Society

Volume 33, Issue 4, December 2018 pp. 427–433.

Finite order elements in the integral symplectic group

**Authors**:
Kumar Balasubramanian, M. Ram Murty and Karam Deo Shankhadhar

**Author institution:**Department of Mathematics, IISER Bhopal, Bhopal, Madhya Pradesh 462 066, India

**Summary: **
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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