Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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
     

   Subscribe/Renew Journal


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.
User
Subscription Login to verify subscription
Notifications
Font Size

  • B. Burgisser, Elements of finite order in symplectic groups, Arch. Math. (Basel), 39 no. 6, (1982) 501–509.

  • Pierre Dusart, Autour de la fonction qui compte le nombre de nombres premiers, Thesis (1998).

  • Pierre Dusart, Estimates of some functions over primes without R.H., arxiv:1002.0442v1.

  • Benson Farb and Dan Margalit, A primer on mapping class groups, Princeton Mathematical Series, vol. 49, Princeton University Press, Princeton, NJ (2012).

  • Barkley Rosser, Explicit bounds for some functions of prime numbers, Amer. J. Math., 63 (1941) 211–232.


Abstract Views: 252

PDF Views: 1




  • Finite Order Elements in the Integral Symplectic Group

Abstract Views: 252  |  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