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• W2085117738 abstract "The principal theme of this paper is the enumeration of finite index subgroups Δ in a free product Γ of finite groups under various restrictions on the isomorphism type of Δ . In particular, we completely resolve the realization, asymptotic, and distribution problems for free products Γ of cyclic groups of prime order (prior to this work, these questions were wide open even in the case of the classical modular group). This complex of problems, usually referred to as Poincaré–Klein Problem, originally arose around 1880 out of the work of Klein and Poincaré on automorphic functions and related number theory, but has also grown roots in geometric function theory and, more recently, in the theory of subgroup growth. Ideas and techniques from the theory of generalized permutation representations (an enumerative theory of wreath product representations recently developed by the first named author) play a fundamental role here. Other tools come from analytic number theory, combinatorics, and probability theory." @default.
• W2085117738 created "2016-06-24" @default.
• W2085117738 creator A5058570102 @default.
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• W2085117738 date "2004-10-01" @default.
• W2085117738 modified "2023-09-24" @default.
• W2085117738 title "Classification and statistics of finite index subgroups in free products" @default.
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• W2085117738 doi "https://doi.org/10.1016/j.aim.2003.09.005" @default.
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