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Thomas W. Müller, Jan-Christoph Schlage-Puchta

Modular arithmetic of free subgroups

Denote by ?_?(G ) the number of free subgroups of index ?m_G , where m_G 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 ?_?(G ), where p is a prime dividing m_G. Among other things, we obtain an explicit combinatorial description of ?_?(G ) modulo p, leading to an optimal generalisation of Stothers’ explicit formula for the parity of ?_?(PSL₂ (?)).

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 05/2005
Pages: 375 - 405

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