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Modular arithmetic of free subgroups
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Thomas W. Müller
Published/Copyright:
July 27, 2005
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)).
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Published Online: 2005-07-27
Published in Print: 2005-05-25
© de Gruyter
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Articles in the same Issue
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- Equivalent expressions for norms in classical Lorentz spaces
- Modular arithmetic of free subgroups
- Complete polynomial vector fields in two complex variables
- 3-dimensional Bol loops as sections in non-solvable Lie groups
- Sharp conditions for weighted Sobolev interpolation inequalities
- Fixed points of pro-tori in cohomology spheres
- Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions
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