3-adic_integers_with_dual_colorings.svg
Summary
Description 3-adic integers with dual colorings.svg |
English:
The
compact group
of
3-adic integers
(black points), with selected elements labeled by the corresponding character on the
Pontryagin dual group
(the
discrete
Prüfer 3-group
) (colored discs).
Counter-clockwise from the right, the labeled elements are 0, 9, 3, 1, −1/8, −1/2, 1/4, −1/4, 1/2, 1/8, −1, −3, and −9. Open the SVG directly in your browser to get tooltips on group elements. Each colored disc is tied to a 3-adic integer, , and it represents the corresponding character on the Prüfer 3-group, , defined by . The circle group used is a color wheel where 0 = red, 1/3 = green, and 2/3 = blue. For details on the embedding of the 3-adic integers, see Chistyakov, D. V. (1996), “Fractal geometry for images of continuous embeddings of p -adic numbers and p -adic 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 1.12. |
Date | |
Source | Own work |
Author | Melchoir |
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