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

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The Growth Spectrumed groups. In earlier chapters we have seen many intermediate types of subgroup growth; we have also seen that among ‘reasonable’ classes of groups, such as linear groups, certain intermediate types cannot occur. If one considers arbitrary finitely generated groups, however, then essentially every t

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Explicit Formulas and Asymptoticshe book, we take a closer look at the numbers .(.) themselves. Of course, the detailed arithmetical and asymptotic properties of this sequence will depend on the nature of the groups . under consideration, as will the methods appropriate to studying them.

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Zeta Functions II: ,-adic Analytic Groupsthe sequence (..(Γ)) is determined in a simple way by the numbers a. (Γ) (for all prime-powers ..); on the other hand, for each fixed prime p the sequence (.. (Γ)) satisfies a linear recurrence relation: in other words, the local . . is a rational function in the variable p.. The first, ‘global’, pr

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Probabilistic Methodsthis means that the measure of a subset . of . is construed as the probability that a random element of . lies in .. It is now natural to ask questions such as: what is the probability that a random .-tuple of elements generates .? Formally, this probability is defined as:P(G,k)= . (11.1)where μ denotes also the product measure on ..

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