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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


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


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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