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
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Mathematical Citation Quotient (MCQ) 2018: 0.71
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Modular arithmetic of free subgroups
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)).
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