%0 Journal Article
%T A nilpotent group without local functional equations for pro-isomorphic subgroups
%A Mark N. Berman
%A Benjamin Klopsch
%J Mathematics
%D 2014
%I arXiv
%X The pro-isomorphic zeta function of a torsion-free finitely generated nilpotent group G enumerates finite index subgroups H such that H and G have isomorphic profinite completions. It admits an Euler product decomposition, indexed by the rational primes. We manufacture the first example of a torsion-free finitely generated nilpotent group G such that the local Euler factors of its pro-isomorphic zeta function do not satisfy functional equations. The group G has nilpotency class 4 and Hirsch length 25. It is obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable algebraic automorphism group Aut(L).
%U http://arxiv.org/abs/1408.6669v1