a1 Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel (email: [email protected])
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
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Supported by ISF and BSF grants.
Dedicated to Cheryl Praeger for her sixtieth birthday