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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 85, Issue 2
  • October 2008, pp. 257-267

THE DENSITY OF SUBGROUP INDICES

  • ANER SHALEV (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788708000943
  • Published online: 01 October 2008
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.

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[1]Peter J. Cameron , Peter M. Neumann and David N. Teague , ‘On the degrees of primitive permutation groups’, Math. Z. 180 (1982), 141149.

[2]Brent Everitt , ‘Alternating quotients of Fuchsian groups’, J. Algebra 223 (2000), 457476.

[4]R. I. Grigorchuk , ‘On Burnside’s problem on periodic groups’, Funktsional Anal. i Prilozhen 14 (1980), 5354.

[6]D. R. Heath-Brown , Cheryl E. Praeger and Aner Shalev , ‘Permutation groups, simple groups, and sieve methods’, Israel J. Math. 148 (2005), 347375. (Furstenberg Volume).

[10]Martin W. Liebeck and Aner Shalev , ‘Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky’, J. Algebra 184 (1996), 3157.

[11]Martin W. Liebeck and Aner Shalev , ‘Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks’, J. Algebra 276 (2004), 552601.

[12]Martin W. Liebeck , Laszlo Pyber and Aner Shalev , ‘On a conjecture of G.E. Wall’, J. Algebra 317 (2007), 184197.

[13]Alexander Lubotzky and Dan Segal , Subgroup Growth, Progress in Mathematics, 212 (Birkhäuser, Basel, 2003).

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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