File:2-adic integers with dual colorings.svg
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editDescription2-adic integers with dual colorings.svg |
English: The compact group of 2-adic integers (black points), with selected elements labeled by the corresponding character on the Pontryagin dual group (the discrete Prüfer 2-group) (colored discs).
Counter-clockwise from the right, the labeled elements are 0, 4, 2, −3, 1, −1/7, −1/3, 1/3, 1/7, −1, 3, −2, and −4. Open the SVG directly in your browser to get tooltips on group elements. Each colored disc is tied to a 2-adic integer, , and it represents the corresponding character on the Prüfer 2-group, , defined by . The circle group is represented by a color wheel where 0 = red. For details on the embedding of the 2-adic integers, see Chistyakov, D. V. (1996), “Fractal geometry for images of continuous embeddings of p-adic numbers and solenoids into Euclidean spaces”, in Theoretical and Mathematical Physics, volume 109, issue 3, DOI:10.1007/BF02073866, pages 1495–1507 The particular mapping used is , defined in Definition 3 and depicted in Figure 1. |
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Source | Own work |
Author | Melchoir |
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