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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 17, Issue 3

Issues

Modular arithmetic of free subgroups

Thomas W. Müller
  • School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK.
  • Other articles by this author:
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/ Jan-Christoph Schlage-Puchta
Published Online: 2005-07-27 | DOI: https://doi.org/10.1515/form.2005.17.3.375

Abstract

Denote by ƒλ (G ) the number of free subgroups of index λmG , where mG is the least common multiple of the orders of the finite subgroups in G. The present paper develops a general theory for the p-divisibility of ƒλ (G ), where p is a prime dividing mG . Among other things, we obtain an explicit combinatorial description of ƒλ (G ) modulo p, leading to an optimal generalisation of Stothers’ explicit formula for the parity of ƒλ (PSL2 (ℤ)).

About the article

Received: 21 March 2003

Published Online: 2005-07-27

Published in Print: 2005-05-25


Citation Information: Forum Mathematicum, Volume 17, Issue 3, Pages 375–405, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2005.17.3.375.

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Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
C. Krattenthaler and T.W. Müller
Journal of Combinatorial Theory, Series A, 2018, Volume 154, Page 49
[2]
C. Krattenthaler and T.W. Müller
Journal of Algebra, 2016, Volume 452, Page 372
[3]
C. Krattenthaler and T.W. Müller
Journal of Combinatorial Theory, Series A, 2013, Volume 120, Number 8, Page 2039
[4]
C. Krattenthaler and Thomas W. Müller
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2008, Volume 78, Number 1, Page 99

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