A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions
The pro-isomorphic zeta function ζ∧Γ(s) of a finitely generated nilpotent group Γ is a Dirichlet generating function that enumerates finite-index subgroups whose profinite completion is isomorphic to that of Γ . Such zeta functions can be expressed as Euler products of p-adic integrals over the Qp -points of an algebraic automorphism group associated to Γ . In this way they are closely related to classical zeta functions of algebraic groups over local fields. We describe the...[Show more]
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