The density of subgroup indices

Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageAmerican English
Pages (from-to)257-267
Number of pages11
JournalJournal of the Australian Mathematical Society
Volume85
Issue number2
DOIs
StatePublished - Oct 2008

Bibliographical note

Funding Information:
Supported by ISF and BSF grants. ©c 2008 Australian Mathematical Society 1446-7887/08 $A2.00 + 0.00

Keywords

  • Essubgroup indices
  • Special linear groups

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