Abstract
We give an exact formula for the number of normal subgroups of each finite index in the Baumslag–Solitar group BS( p, q ) when p and q are coprime. Unlike the formula for all finite index subgroups, this one distinguishes different Baumslag–Solitar groups and is not multiplicative. This allows us to give an example of a finitely generated profinite group which is not virtually pronilpotent but whose zeta function has an Euler product.
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