ZETA FUNCTION OF REPRESENTATIONS OF COMPACT p-ADIC ANALYTIC GROUPS
نویسنده
چکیده
Let G be a profinite group. We denote by rn(G) the number of isomorphism classes of irreducible n-dimensional complex continuous representations of G (so that the kernel is open in G). Following [20], we call rn(G) the representation growth function of G. If G is a finitely generated profinite group, then rn(G) < ∞ for every n if and only if G has the property FAb (that is, H/[H,H] is finite for every open subgroup H of G) [1, Proposition 2]. In the case when G is a finitely generated pro-p group, the property FAb is equivalent to the condition that all derived subgroups G are open. In this paper we shall investigate the function
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