Skip to main content
×
Home

THE DENSITY OF SUBGROUP INDICES

  • ANER SHALEV (a1)
Abstract
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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      THE DENSITY OF SUBGROUP INDICES
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      THE DENSITY OF SUBGROUP INDICES
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      THE DENSITY OF SUBGROUP INDICES
      Available formats
      ×
Copyright
References
Hide All
[1]Cameron Peter J., Neumann Peter M. and Teague David N., ‘On the degrees of primitive permutation groups’, Math. Z. 180 (1982), 141149.
[2]Everitt Brent, ‘Alternating quotients of Fuchsian groups’, J. Algebra 223 (2000), 457476.
[3]Golod E. S., ‘On nil-algebras and finitely approximable p-groups’, Izv. Akad. Nauk. SSSR Ser. Mat. 28 (1964), 273276.
[4]Grigorchuk R. I., ‘On Burnside’s problem on periodic groups’, Funktsional Anal. i Prilozhen 14 (1980), 5354.
[5]Hardy G. H. and Wright E. M., An Introduction to the Theory of Numbers, 5th edn (Oxford University Press, New York, 1979).
[6]Heath-Brown D. R., Praeger Cheryl E. and Shalev Aner, ‘Permutation groups, simple groups, and sieve methods’, Israel J. Math. 148 (2005), 347375. (Furstenberg Volume).
[7]Kassabov Martin and Nikolov Nikolay, ‘Cartesian products as profinite completions’, Int. Math. Res. Not., ID 72947 (2006), 17 pp.
[8]Kleidman Peter and Liebeck Martin, The Subgroup Structure of the Finite Classical Groups, London Mathematical Society Lecture Note Series, 129 (Cambridge University Press, Cambridge, 1990).
[9]Liebeck Martin  W. and Saxl Jan, ‘On the orders of maximal subgroups of the finite simple exceptional groups of Lie type’, Proc. London Math. Soc. 55 (1987), 299330.
[10]Liebeck Martin W. and Shalev Aner, ‘Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky’, J. Algebra 184 (1996), 3157.
[11]Liebeck Martin W. and Shalev Aner, ‘Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks’, J. Algebra 276 (2004), 552601.
[12]Liebeck Martin W., Pyber Laszlo and Shalev Aner, ‘On a conjecture of G.E. Wall’, J. Algebra 317 (2007), 184197.
[13]Lubotzky Alexander and Segal Dan, Subgroup Growth, Progress in Mathematics, 212 (Birkhäuser, Basel, 2003).
[14]Nikolov Nikolay, Strong approximation methods in group theory — LMS/EPSRC short course, (2007). arxiv:math.GR 0803.4165v2.
[15]Shalev Aner, The density of subgroup indices, II, in preparation.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 36 *
Loading metrics...

Abstract views

Total abstract views: 36 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th November 2017. This data will be updated every 24 hours.