Titlebook: Subgroup Growth; Alexander Lubotzky,Dan Segal Book 2003 Birkhäuser Verlag 2003 Abelian group.Algebra.Algebraic structure.Group theory.Prim

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Free Groups. By considering homomorphisms of a .-generator group . into Sym(.), we showed in §1.1 that .(.) ≤ . · (.!). for each .. It is not much harder to see that asymptotically this bound is achieved. Rather surprisingly, the same applies also to the number .(.) of maximal subgroups of index .. The precise

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Groups with Exponential Subgroup Growthy exponential type is certainly some kind of restriction. Can it be characterized algebraically? This question seems difficult to answer, because the groups with exponential subgroup growth encompass a huge variety of examples. This is not really surprising, because a very mild algebraic condition i

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The Generalized Congruence Subgroup Problemses of valuations) of . is denoted ., the finite subset of ‘infinite primes’ (archimedean valuations) is .∞, and ..∞ = .; so . may be identified with the set of non-zero prime ideals of .. For each υ ∈ . the υ-completion of . is denoted ..

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Profinite Groups with Polynomial Subgroup Growth of finite rank. The proof involved two kinds of argument: a ‘local’ part, analysing the finite quotients of the group, and a ‘global’ part which involved representing the group as a linear group. The latter depended crucially on the group being finitely generated, and the result is not true without

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