Abstract
Abstract We construct a 2-generated pro-2 group with full normal Hausdorff spectrum [ 0 , 1 ] [0,1] , with respect to each of the four standard filtration series: the 2-power series, the lower 2-series, the Frattini series, and the dimension subgroup series. This answers a question of Klopsch and the second author, for the even prime case; the odd prime case was settled by the first author and Klopsch. Also, our construction gives the first example of a finitely generated pro-2 group with full Hausdorff spectrum with respect to the lower 2-series.
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