Journal of the Australian Mathematical Society

Research Article

THE DENSITY OF SUBGROUP INDICES

ANER SHALEVa1

a1 Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel (email: shalev@math.huji.ac.il)

Abstract

For a group G and a real number x≥1 we let sG(x) denote the number of indices ≤x of subgroups of G. We call the function sG the subgroup density of G, and initiate a study of its asymptotics and its relation to the algebraic structure of G. We also count indices ≤x of maximal subgroups of G, and relate it to symmetric and alternating quotients of G.

(Received April 10 2008)

(Accepted May 08 2008)

2000 Mathematics subject classification

  • 20E07;
  • 20F69

Keywords and phrases

  • subgroup indices;
  • special linear groups

Footnotes

Supported by ISF and BSF grants.

Dedicated to Cheryl Praeger for her sixtieth birthday