鬼魂 发表于 2025-3-30 08:42:53
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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性别 发表于 2025-3-30 19:24:32
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.ADJ 发表于 2025-3-30 21:21:41
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’, prPanacea 发表于 2025-3-31 04:11:24
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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 ..Offensive 发表于 2025-3-31 12:40:22
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